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1 | 2890-2893 | The actual
values of the internal resistances of cells vary from cell to cell The internal
resistance of dry cells, however, is much higher than the common
electrolytic cells We also observe that since V is the potential difference across R, we
have from Ohm’s law
V = I R
(3 39)
Combining Eqs |
1 | 2891-2894 | The internal
resistance of dry cells, however, is much higher than the common
electrolytic cells We also observe that since V is the potential difference across R, we
have from Ohm’s law
V = I R
(3 39)
Combining Eqs (3 |
1 | 2892-2895 | We also observe that since V is the potential difference across R, we
have from Ohm’s law
V = I R
(3 39)
Combining Eqs (3 38) and (3 |
1 | 2893-2896 | 39)
Combining Eqs (3 38) and (3 39), we get
FIGURE 3 |
1 | 2894-2897 | (3 38) and (3 39), we get
FIGURE 3 12 (a) Sketch of
an electrolyte cell with
positive terminal P and
negative terminal N |
1 | 2895-2898 | 38) and (3 39), we get
FIGURE 3 12 (a) Sketch of
an electrolyte cell with
positive terminal P and
negative terminal N The
gap between the electrodes
is exaggerated for clarity |
1 | 2896-2899 | 39), we get
FIGURE 3 12 (a) Sketch of
an electrolyte cell with
positive terminal P and
negative terminal N The
gap between the electrodes
is exaggerated for clarity A
and B are points in the
electrolyte typically close to
P and N |
1 | 2897-2900 | 12 (a) Sketch of
an electrolyte cell with
positive terminal P and
negative terminal N The
gap between the electrodes
is exaggerated for clarity A
and B are points in the
electrolyte typically close to
P and N (b) the symbol for
a cell, + referring to P and
– referring to the N
electrode |
1 | 2898-2901 | The
gap between the electrodes
is exaggerated for clarity A
and B are points in the
electrolyte typically close to
P and N (b) the symbol for
a cell, + referring to P and
– referring to the N
electrode Electrical
connections to the cell are
made at P and N |
1 | 2899-2902 | A
and B are points in the
electrolyte typically close to
P and N (b) the symbol for
a cell, + referring to P and
– referring to the N
electrode Electrical
connections to the cell are
made at P and N Rationalised 2023-24
Current
Electricity
95
I R = e – I r
Or, I
R
r
=
ε+
(3 |
1 | 2900-2903 | (b) the symbol for
a cell, + referring to P and
– referring to the N
electrode Electrical
connections to the cell are
made at P and N Rationalised 2023-24
Current
Electricity
95
I R = e – I r
Or, I
R
r
=
ε+
(3 40)
The maximum current that can be drawn from a cell is for R = 0 and
it is Imax = e/r |
1 | 2901-2904 | Electrical
connections to the cell are
made at P and N Rationalised 2023-24
Current
Electricity
95
I R = e – I r
Or, I
R
r
=
ε+
(3 40)
The maximum current that can be drawn from a cell is for R = 0 and
it is Imax = e/r However, in most cells the maximum allowed current is
much lower than this to prevent permanent damage to the cell |
1 | 2902-2905 | Rationalised 2023-24
Current
Electricity
95
I R = e – I r
Or, I
R
r
=
ε+
(3 40)
The maximum current that can be drawn from a cell is for R = 0 and
it is Imax = e/r However, in most cells the maximum allowed current is
much lower than this to prevent permanent damage to the cell 3 |
1 | 2903-2906 | 40)
The maximum current that can be drawn from a cell is for R = 0 and
it is Imax = e/r However, in most cells the maximum allowed current is
much lower than this to prevent permanent damage to the cell 3 11 CELLS IN SERIES AND IN PARALLEL
Like resistors, cells can be combined together in an electric circuit |
1 | 2904-2907 | However, in most cells the maximum allowed current is
much lower than this to prevent permanent damage to the cell 3 11 CELLS IN SERIES AND IN PARALLEL
Like resistors, cells can be combined together in an electric circuit And
like resistors, one can, for calculating currents and voltages in a circuit,
replace a combination of cells by an equivalent cell |
1 | 2905-2908 | 3 11 CELLS IN SERIES AND IN PARALLEL
Like resistors, cells can be combined together in an electric circuit And
like resistors, one can, for calculating currents and voltages in a circuit,
replace a combination of cells by an equivalent cell FIGURE 3 |
1 | 2906-2909 | 11 CELLS IN SERIES AND IN PARALLEL
Like resistors, cells can be combined together in an electric circuit And
like resistors, one can, for calculating currents and voltages in a circuit,
replace a combination of cells by an equivalent cell FIGURE 3 13 Two cells of emf’s e1 and e2 in the series |
1 | 2907-2910 | And
like resistors, one can, for calculating currents and voltages in a circuit,
replace a combination of cells by an equivalent cell FIGURE 3 13 Two cells of emf’s e1 and e2 in the series r1, r2 are their
internal resistances |
1 | 2908-2911 | FIGURE 3 13 Two cells of emf’s e1 and e2 in the series r1, r2 are their
internal resistances For connections across A and C, the combination
can be considered as one cell of emf eeq and an internal resistance req |
1 | 2909-2912 | 13 Two cells of emf’s e1 and e2 in the series r1, r2 are their
internal resistances For connections across A and C, the combination
can be considered as one cell of emf eeq and an internal resistance req Consider first two cells in series (Fig |
1 | 2910-2913 | r1, r2 are their
internal resistances For connections across A and C, the combination
can be considered as one cell of emf eeq and an internal resistance req Consider first two cells in series (Fig 3 |
1 | 2911-2914 | For connections across A and C, the combination
can be considered as one cell of emf eeq and an internal resistance req Consider first two cells in series (Fig 3 13), where one terminal of the
two cells is joined together leaving the other terminal in either cell free |
1 | 2912-2915 | Consider first two cells in series (Fig 3 13), where one terminal of the
two cells is joined together leaving the other terminal in either cell free e1, e2 are the emf’s of the two cells and r1, r2 their internal resistances,
respectively |
1 | 2913-2916 | 3 13), where one terminal of the
two cells is joined together leaving the other terminal in either cell free e1, e2 are the emf’s of the two cells and r1, r2 their internal resistances,
respectively Let V (A), V (B), V (C) be the potentials at points A, B and C shown in
Fig |
1 | 2914-2917 | 13), where one terminal of the
two cells is joined together leaving the other terminal in either cell free e1, e2 are the emf’s of the two cells and r1, r2 their internal resistances,
respectively Let V (A), V (B), V (C) be the potentials at points A, B and C shown in
Fig 3 |
1 | 2915-2918 | e1, e2 are the emf’s of the two cells and r1, r2 their internal resistances,
respectively Let V (A), V (B), V (C) be the potentials at points A, B and C shown in
Fig 3 13 |
1 | 2916-2919 | Let V (A), V (B), V (C) be the potentials at points A, B and C shown in
Fig 3 13 Then V (A) – V (B) is the potential difference between the positive
and negative terminals of the first cell |
1 | 2917-2920 | 3 13 Then V (A) – V (B) is the potential difference between the positive
and negative terminals of the first cell We have already calculated it in
Eq |
1 | 2918-2921 | 13 Then V (A) – V (B) is the potential difference between the positive
and negative terminals of the first cell We have already calculated it in
Eq (3 |
1 | 2919-2922 | Then V (A) – V (B) is the potential difference between the positive
and negative terminals of the first cell We have already calculated it in
Eq (3 38) and hence,
V
V
V
I r
AB
A
B
≡
=
(
) �
( )
ε1�
1
(3 |
1 | 2920-2923 | We have already calculated it in
Eq (3 38) and hence,
V
V
V
I r
AB
A
B
≡
=
(
) �
( )
ε1�
1
(3 41)
Similarly,
V
V
V
I r
BC
B
C
≡
=
( ) �
( )
ε2�
2
(3 |
1 | 2921-2924 | (3 38) and hence,
V
V
V
I r
AB
A
B
≡
=
(
) �
( )
ε1�
1
(3 41)
Similarly,
V
V
V
I r
BC
B
C
≡
=
( ) �
( )
ε2�
2
(3 42)
Hence, the potential difference between the terminals A and C of the
combination is
( )
( )
( )
( )
AC
(A)–
(C)
A –
B
B –
C
V
V
V
V
V
V
V
≡
=
+
(
)
(
)
1
2
1
2
– I r
r
ε
ε
=
+
+
(3 |
1 | 2922-2925 | 38) and hence,
V
V
V
I r
AB
A
B
≡
=
(
) �
( )
ε1�
1
(3 41)
Similarly,
V
V
V
I r
BC
B
C
≡
=
( ) �
( )
ε2�
2
(3 42)
Hence, the potential difference between the terminals A and C of the
combination is
( )
( )
( )
( )
AC
(A)–
(C)
A –
B
B –
C
V
V
V
V
V
V
V
≡
=
+
(
)
(
)
1
2
1
2
– I r
r
ε
ε
=
+
+
(3 43)
If we wish to replace the combination by a single cell between A and
C of emf eeq and internal resistance req, we would have
VAC = eeq– I req
(3 |
1 | 2923-2926 | 41)
Similarly,
V
V
V
I r
BC
B
C
≡
=
( ) �
( )
ε2�
2
(3 42)
Hence, the potential difference between the terminals A and C of the
combination is
( )
( )
( )
( )
AC
(A)–
(C)
A –
B
B –
C
V
V
V
V
V
V
V
≡
=
+
(
)
(
)
1
2
1
2
– I r
r
ε
ε
=
+
+
(3 43)
If we wish to replace the combination by a single cell between A and
C of emf eeq and internal resistance req, we would have
VAC = eeq– I req
(3 44)
Comparing the last two equations, we get
eeq = e1 + e2
(3 |
1 | 2924-2927 | 42)
Hence, the potential difference between the terminals A and C of the
combination is
( )
( )
( )
( )
AC
(A)–
(C)
A –
B
B –
C
V
V
V
V
V
V
V
≡
=
+
(
)
(
)
1
2
1
2
– I r
r
ε
ε
=
+
+
(3 43)
If we wish to replace the combination by a single cell between A and
C of emf eeq and internal resistance req, we would have
VAC = eeq– I req
(3 44)
Comparing the last two equations, we get
eeq = e1 + e2
(3 45)
and req = r1 + r2
(3 |
1 | 2925-2928 | 43)
If we wish to replace the combination by a single cell between A and
C of emf eeq and internal resistance req, we would have
VAC = eeq– I req
(3 44)
Comparing the last two equations, we get
eeq = e1 + e2
(3 45)
and req = r1 + r2
(3 46)
In Fig |
1 | 2926-2929 | 44)
Comparing the last two equations, we get
eeq = e1 + e2
(3 45)
and req = r1 + r2
(3 46)
In Fig 3 |
1 | 2927-2930 | 45)
and req = r1 + r2
(3 46)
In Fig 3 13, we had connected the negative electrode of the first to the
positive electrode of the second |
1 | 2928-2931 | 46)
In Fig 3 13, we had connected the negative electrode of the first to the
positive electrode of the second If instead we connect the two negatives,
Rationalised 2023-24
Physics
96
Eq |
1 | 2929-2932 | 3 13, we had connected the negative electrode of the first to the
positive electrode of the second If instead we connect the two negatives,
Rationalised 2023-24
Physics
96
Eq (3 |
1 | 2930-2933 | 13, we had connected the negative electrode of the first to the
positive electrode of the second If instead we connect the two negatives,
Rationalised 2023-24
Physics
96
Eq (3 42) would change to VBC = –e2–Ir2 and we will get
eeq = e1 – e2 (e1 > e2)
(3 |
1 | 2931-2934 | If instead we connect the two negatives,
Rationalised 2023-24
Physics
96
Eq (3 42) would change to VBC = –e2–Ir2 and we will get
eeq = e1 – e2 (e1 > e2)
(3 47)
The rule for series combination clearly can be extended to any number
of cells:
(i)
The equivalent emf of a series combination of n cells is just the sum of
their individual emf’s, and
(ii) The equivalent internal resistance of a series combination of n cells is
just the sum of their internal resistances |
1 | 2932-2935 | (3 42) would change to VBC = –e2–Ir2 and we will get
eeq = e1 – e2 (e1 > e2)
(3 47)
The rule for series combination clearly can be extended to any number
of cells:
(i)
The equivalent emf of a series combination of n cells is just the sum of
their individual emf’s, and
(ii) The equivalent internal resistance of a series combination of n cells is
just the sum of their internal resistances This is so, when the current leaves each cell from the positive
electrode |
1 | 2933-2936 | 42) would change to VBC = –e2–Ir2 and we will get
eeq = e1 – e2 (e1 > e2)
(3 47)
The rule for series combination clearly can be extended to any number
of cells:
(i)
The equivalent emf of a series combination of n cells is just the sum of
their individual emf’s, and
(ii) The equivalent internal resistance of a series combination of n cells is
just the sum of their internal resistances This is so, when the current leaves each cell from the positive
electrode If in the combination, the current leaves any cell from
the negative electrode, the emf of the cell enters the expression
for eeq with a negative sign, as in Eq |
1 | 2934-2937 | 47)
The rule for series combination clearly can be extended to any number
of cells:
(i)
The equivalent emf of a series combination of n cells is just the sum of
their individual emf’s, and
(ii) The equivalent internal resistance of a series combination of n cells is
just the sum of their internal resistances This is so, when the current leaves each cell from the positive
electrode If in the combination, the current leaves any cell from
the negative electrode, the emf of the cell enters the expression
for eeq with a negative sign, as in Eq (3 |
1 | 2935-2938 | This is so, when the current leaves each cell from the positive
electrode If in the combination, the current leaves any cell from
the negative electrode, the emf of the cell enters the expression
for eeq with a negative sign, as in Eq (3 47) |
1 | 2936-2939 | If in the combination, the current leaves any cell from
the negative electrode, the emf of the cell enters the expression
for eeq with a negative sign, as in Eq (3 47) Next, consider a parallel combination of the cells (Fig |
1 | 2937-2940 | (3 47) Next, consider a parallel combination of the cells (Fig 3 |
1 | 2938-2941 | 47) Next, consider a parallel combination of the cells (Fig 3 14) |
1 | 2939-2942 | Next, consider a parallel combination of the cells (Fig 3 14) I1 and I2 are the currents leaving the positive electrodes of the
cells |
1 | 2940-2943 | 3 14) I1 and I2 are the currents leaving the positive electrodes of the
cells At the point B1, I1 and I2 flow in whereas the current I flows
out |
1 | 2941-2944 | 14) I1 and I2 are the currents leaving the positive electrodes of the
cells At the point B1, I1 and I2 flow in whereas the current I flows
out Since as much charge flows in as out, we have
I = I1 + I2
(3 |
1 | 2942-2945 | I1 and I2 are the currents leaving the positive electrodes of the
cells At the point B1, I1 and I2 flow in whereas the current I flows
out Since as much charge flows in as out, we have
I = I1 + I2
(3 48)
Let V (B1) and V (B2) be the potentials at B1 and B2, respectively |
1 | 2943-2946 | At the point B1, I1 and I2 flow in whereas the current I flows
out Since as much charge flows in as out, we have
I = I1 + I2
(3 48)
Let V (B1) and V (B2) be the potentials at B1 and B2, respectively Then, considering the first cell, the potential difference across its
terminals is V (B1) – V (B2) |
1 | 2944-2947 | Since as much charge flows in as out, we have
I = I1 + I2
(3 48)
Let V (B1) and V (B2) be the potentials at B1 and B2, respectively Then, considering the first cell, the potential difference across its
terminals is V (B1) – V (B2) Hence, from Eq |
1 | 2945-2948 | 48)
Let V (B1) and V (B2) be the potentials at B1 and B2, respectively Then, considering the first cell, the potential difference across its
terminals is V (B1) – V (B2) Hence, from Eq (3 |
1 | 2946-2949 | Then, considering the first cell, the potential difference across its
terminals is V (B1) – V (B2) Hence, from Eq (3 38)
(
)
(
)
1
2
1
1 1
–
–
V
V B
V B
I r
ε
≡
=
(3 |
1 | 2947-2950 | Hence, from Eq (3 38)
(
)
(
)
1
2
1
1 1
–
–
V
V B
V B
I r
ε
≡
=
(3 49)
Points B1 and B2 are connected exactly similarly to the second
cell |
1 | 2948-2951 | (3 38)
(
)
(
)
1
2
1
1 1
–
–
V
V B
V B
I r
ε
≡
=
(3 49)
Points B1 and B2 are connected exactly similarly to the second
cell Hence considering the second cell, we also have
(
)
(
)
1
2
2
2 2
–
–
V
V B
V B
I r
ε
≡
=
(3 |
1 | 2949-2952 | 38)
(
)
(
)
1
2
1
1 1
–
–
V
V B
V B
I r
ε
≡
=
(3 49)
Points B1 and B2 are connected exactly similarly to the second
cell Hence considering the second cell, we also have
(
)
(
)
1
2
2
2 2
–
–
V
V B
V B
I r
ε
≡
=
(3 50)
Combining the last three equations
1
2
I
I
I
=
+
=
+
=
+
+
ε
ε
ε
ε
1
1
2
2
1
1
2
2
1
2
1
1
–
–
–
rV
rV
r
r
V
r
r
(3 |
1 | 2950-2953 | 49)
Points B1 and B2 are connected exactly similarly to the second
cell Hence considering the second cell, we also have
(
)
(
)
1
2
2
2 2
–
–
V
V B
V B
I r
ε
≡
=
(3 50)
Combining the last three equations
1
2
I
I
I
=
+
=
+
=
+
+
ε
ε
ε
ε
1
1
2
2
1
1
2
2
1
2
1
1
–
–
–
rV
rV
r
r
V
r
r
(3 51)
Hence, V is given by,
1 2
2 1
1 2
1
2
1
2
–
r
r
r r
V
I
r
r
r
r
ε
+ε
=
+
+
(3 |
1 | 2951-2954 | Hence considering the second cell, we also have
(
)
(
)
1
2
2
2 2
–
–
V
V B
V B
I r
ε
≡
=
(3 50)
Combining the last three equations
1
2
I
I
I
=
+
=
+
=
+
+
ε
ε
ε
ε
1
1
2
2
1
1
2
2
1
2
1
1
–
–
–
rV
rV
r
r
V
r
r
(3 51)
Hence, V is given by,
1 2
2 1
1 2
1
2
1
2
–
r
r
r r
V
I
r
r
r
r
ε
+ε
=
+
+
(3 52)
If we want to replace the combination by a single cell, between B1 and
B2, of emf eeq and internal resistance req, we would have
V = eeq – I req
(3 |
1 | 2952-2955 | 50)
Combining the last three equations
1
2
I
I
I
=
+
=
+
=
+
+
ε
ε
ε
ε
1
1
2
2
1
1
2
2
1
2
1
1
–
–
–
rV
rV
r
r
V
r
r
(3 51)
Hence, V is given by,
1 2
2 1
1 2
1
2
1
2
–
r
r
r r
V
I
r
r
r
r
ε
+ε
=
+
+
(3 52)
If we want to replace the combination by a single cell, between B1 and
B2, of emf eeq and internal resistance req, we would have
V = eeq – I req
(3 53)
The last two equations should be the same and hence
1 2
2 1
1
2
eq
r
r
r
r
ε
ε
ε
+
=
+
(3 |
1 | 2953-2956 | 51)
Hence, V is given by,
1 2
2 1
1 2
1
2
1
2
–
r
r
r r
V
I
r
r
r
r
ε
+ε
=
+
+
(3 52)
If we want to replace the combination by a single cell, between B1 and
B2, of emf eeq and internal resistance req, we would have
V = eeq – I req
(3 53)
The last two equations should be the same and hence
1 2
2 1
1
2
eq
r
r
r
r
ε
ε
ε
+
=
+
(3 54)
1 2
1
2
eq
r r
r
r
r
=
+
(3 |
1 | 2954-2957 | 52)
If we want to replace the combination by a single cell, between B1 and
B2, of emf eeq and internal resistance req, we would have
V = eeq – I req
(3 53)
The last two equations should be the same and hence
1 2
2 1
1
2
eq
r
r
r
r
ε
ε
ε
+
=
+
(3 54)
1 2
1
2
eq
r r
r
r
r
=
+
(3 55)
We can put these equations in a simpler way,
FIGURE 3 |
1 | 2955-2958 | 53)
The last two equations should be the same and hence
1 2
2 1
1
2
eq
r
r
r
r
ε
ε
ε
+
=
+
(3 54)
1 2
1
2
eq
r r
r
r
r
=
+
(3 55)
We can put these equations in a simpler way,
FIGURE 3 14 Two cells in
parallel |
1 | 2956-2959 | 54)
1 2
1
2
eq
r r
r
r
r
=
+
(3 55)
We can put these equations in a simpler way,
FIGURE 3 14 Two cells in
parallel For connections
across A and C, the
combination can be
replaced by one cell of emf
eeq and internal resistances
req whose values are given in
Eqs |
1 | 2957-2960 | 55)
We can put these equations in a simpler way,
FIGURE 3 14 Two cells in
parallel For connections
across A and C, the
combination can be
replaced by one cell of emf
eeq and internal resistances
req whose values are given in
Eqs (3 |
1 | 2958-2961 | 14 Two cells in
parallel For connections
across A and C, the
combination can be
replaced by one cell of emf
eeq and internal resistances
req whose values are given in
Eqs (3 54) and (3 |
1 | 2959-2962 | For connections
across A and C, the
combination can be
replaced by one cell of emf
eeq and internal resistances
req whose values are given in
Eqs (3 54) and (3 55) |
1 | 2960-2963 | (3 54) and (3 55) Rationalised 2023-24
Current
Electricity
97
1
2
1
1
1
req
r
r
=
+
(3 |
1 | 2961-2964 | 54) and (3 55) Rationalised 2023-24
Current
Electricity
97
1
2
1
1
1
req
r
r
=
+
(3 56)
1
2
1
2
eq
req
r
r
ε
ε
ε
=
+
(3 |
1 | 2962-2965 | 55) Rationalised 2023-24
Current
Electricity
97
1
2
1
1
1
req
r
r
=
+
(3 56)
1
2
1
2
eq
req
r
r
ε
ε
ε
=
+
(3 57)
In Fig |
1 | 2963-2966 | Rationalised 2023-24
Current
Electricity
97
1
2
1
1
1
req
r
r
=
+
(3 56)
1
2
1
2
eq
req
r
r
ε
ε
ε
=
+
(3 57)
In Fig (3 |
1 | 2964-2967 | 56)
1
2
1
2
eq
req
r
r
ε
ε
ε
=
+
(3 57)
In Fig (3 14), we had joined the positive terminals
together and similarly the two negative ones, so that the
currents I1, I2 flow out of positive terminals |
1 | 2965-2968 | 57)
In Fig (3 14), we had joined the positive terminals
together and similarly the two negative ones, so that the
currents I1, I2 flow out of positive terminals If the negative
terminal of the second is connected to positive terminal
of the first, Eqs |
1 | 2966-2969 | (3 14), we had joined the positive terminals
together and similarly the two negative ones, so that the
currents I1, I2 flow out of positive terminals If the negative
terminal of the second is connected to positive terminal
of the first, Eqs (3 |
1 | 2967-2970 | 14), we had joined the positive terminals
together and similarly the two negative ones, so that the
currents I1, I2 flow out of positive terminals If the negative
terminal of the second is connected to positive terminal
of the first, Eqs (3 56) and (3 |
1 | 2968-2971 | If the negative
terminal of the second is connected to positive terminal
of the first, Eqs (3 56) and (3 57) would still be valid with
e 2 ® –e2
Equations (3 |
1 | 2969-2972 | (3 56) and (3 57) would still be valid with
e 2 ® –e2
Equations (3 56) and (3 |
1 | 2970-2973 | 56) and (3 57) would still be valid with
e 2 ® –e2
Equations (3 56) and (3 57) can be extended easily |
1 | 2971-2974 | 57) would still be valid with
e 2 ® –e2
Equations (3 56) and (3 57) can be extended easily If there are n cells of emf e1, |
1 | 2972-2975 | 56) and (3 57) can be extended easily If there are n cells of emf e1, en and of internal
resistances r1, |
1 | 2973-2976 | 57) can be extended easily If there are n cells of emf e1, en and of internal
resistances r1, rn respectively, connected in parallel, the
combination is equivalent to a single cell of emf eeq and
internal resistance req, such that
1
1
1
1
r
r
r
eq
n
=
+ |
1 | 2974-2977 | If there are n cells of emf e1, en and of internal
resistances r1, rn respectively, connected in parallel, the
combination is equivalent to a single cell of emf eeq and
internal resistance req, such that
1
1
1
1
r
r
r
eq
n
=
+ +
(3 |
1 | 2975-2978 | en and of internal
resistances r1, rn respectively, connected in parallel, the
combination is equivalent to a single cell of emf eeq and
internal resistance req, such that
1
1
1
1
r
r
r
eq
n
=
+ +
(3 58)
ε
ε
ε
eq
eq
n
n
r
r
r
=
+
+
1
1 |
1 | 2976-2979 | rn respectively, connected in parallel, the
combination is equivalent to a single cell of emf eeq and
internal resistance req, such that
1
1
1
1
r
r
r
eq
n
=
+ +
(3 58)
ε
ε
ε
eq
eq
n
n
r
r
r
=
+
+
1
1 (3 |
1 | 2977-2980 | +
(3 58)
ε
ε
ε
eq
eq
n
n
r
r
r
=
+
+
1
1 (3 59)
3 |
1 | 2978-2981 | 58)
ε
ε
ε
eq
eq
n
n
r
r
r
=
+
+
1
1 (3 59)
3 12 KIRCHHOFF’S RULES
Electric circuits generally consist of a number of resistors
and cells interconnected sometimes in a complicated way |
1 | 2979-2982 | (3 59)
3 12 KIRCHHOFF’S RULES
Electric circuits generally consist of a number of resistors
and cells interconnected sometimes in a complicated way The formulae we have derived earlier for series and parallel combinations
of resistors are not always sufficient to determine all the currents and
potential differences in the circuit |
1 | 2980-2983 | 59)
3 12 KIRCHHOFF’S RULES
Electric circuits generally consist of a number of resistors
and cells interconnected sometimes in a complicated way The formulae we have derived earlier for series and parallel combinations
of resistors are not always sufficient to determine all the currents and
potential differences in the circuit Two rules, called Kirchhoff’s rules,
are very useful for analysis of electric circuits |
1 | 2981-2984 | 12 KIRCHHOFF’S RULES
Electric circuits generally consist of a number of resistors
and cells interconnected sometimes in a complicated way The formulae we have derived earlier for series and parallel combinations
of resistors are not always sufficient to determine all the currents and
potential differences in the circuit Two rules, called Kirchhoff’s rules,
are very useful for analysis of electric circuits Given a circuit, we start by labelling currents in each resistor by a
symbol, say I, and a directed arrow to indicate that a current I flows
along the resistor in the direction indicated |
1 | 2982-2985 | The formulae we have derived earlier for series and parallel combinations
of resistors are not always sufficient to determine all the currents and
potential differences in the circuit Two rules, called Kirchhoff’s rules,
are very useful for analysis of electric circuits Given a circuit, we start by labelling currents in each resistor by a
symbol, say I, and a directed arrow to indicate that a current I flows
along the resistor in the direction indicated If ultimately I is determined
to be positive, the actual current in the resistor is in the direction of the
arrow |
1 | 2983-2986 | Two rules, called Kirchhoff’s rules,
are very useful for analysis of electric circuits Given a circuit, we start by labelling currents in each resistor by a
symbol, say I, and a directed arrow to indicate that a current I flows
along the resistor in the direction indicated If ultimately I is determined
to be positive, the actual current in the resistor is in the direction of the
arrow If I turns out to be negative, the current actually flows in a direction
opposite to the arrow |
1 | 2984-2987 | Given a circuit, we start by labelling currents in each resistor by a
symbol, say I, and a directed arrow to indicate that a current I flows
along the resistor in the direction indicated If ultimately I is determined
to be positive, the actual current in the resistor is in the direction of the
arrow If I turns out to be negative, the current actually flows in a direction
opposite to the arrow Similarly, for each source (i |
1 | 2985-2988 | If ultimately I is determined
to be positive, the actual current in the resistor is in the direction of the
arrow If I turns out to be negative, the current actually flows in a direction
opposite to the arrow Similarly, for each source (i e |
1 | 2986-2989 | If I turns out to be negative, the current actually flows in a direction
opposite to the arrow Similarly, for each source (i e , cell or some other
source of electrical power) the positive and negative electrodes are labelled,
as well as, a directed arrow with a symbol for the current flowing through
the cell |
1 | 2987-2990 | Similarly, for each source (i e , cell or some other
source of electrical power) the positive and negative electrodes are labelled,
as well as, a directed arrow with a symbol for the current flowing through
the cell This will tell us the potential difference, V = V (P) – V (N) = e – I r
[Eq |
1 | 2988-2991 | e , cell or some other
source of electrical power) the positive and negative electrodes are labelled,
as well as, a directed arrow with a symbol for the current flowing through
the cell This will tell us the potential difference, V = V (P) – V (N) = e – I r
[Eq (3 |
1 | 2989-2992 | , cell or some other
source of electrical power) the positive and negative electrodes are labelled,
as well as, a directed arrow with a symbol for the current flowing through
the cell This will tell us the potential difference, V = V (P) – V (N) = e – I r
[Eq (3 38) between the positive terminal P and the negative terminal N; I
here is the current flowing from N to P through the cell] |
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