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1 | 2690-2693 | The deviations broadly are one or more of the following
types:
(a) V ceases to be proportional to I (Fig 3 5) (b) The relation between V and I depends on the sign of V |
1 | 2691-2694 | 3 5) (b) The relation between V and I depends on the sign of V In
other words, if I is the current for a certain V, then reversing
the direction of V keeping its magnitude fixed, does not
produce a current of the same magnitude as I in the opposite direction
(Fig |
1 | 2692-2695 | 5) (b) The relation between V and I depends on the sign of V In
other words, if I is the current for a certain V, then reversing
the direction of V keeping its magnitude fixed, does not
produce a current of the same magnitude as I in the opposite direction
(Fig 3 |
1 | 2693-2696 | (b) The relation between V and I depends on the sign of V In
other words, if I is the current for a certain V, then reversing
the direction of V keeping its magnitude fixed, does not
produce a current of the same magnitude as I in the opposite direction
(Fig 3 6) |
1 | 2694-2697 | In
other words, if I is the current for a certain V, then reversing
the direction of V keeping its magnitude fixed, does not
produce a current of the same magnitude as I in the opposite direction
(Fig 3 6) This happens, for example, in a diode which we will study
in Chapter 14 |
1 | 2695-2698 | 3 6) This happens, for example, in a diode which we will study
in Chapter 14 (c) The relation between V and I is not unique, i |
1 | 2696-2699 | 6) This happens, for example, in a diode which we will study
in Chapter 14 (c) The relation between V and I is not unique, i e |
1 | 2697-2700 | This happens, for example, in a diode which we will study
in Chapter 14 (c) The relation between V and I is not unique, i e , there is more than
one value of V for the same current I (Fig |
1 | 2698-2701 | (c) The relation between V and I is not unique, i e , there is more than
one value of V for the same current I (Fig 3 |
1 | 2699-2702 | e , there is more than
one value of V for the same current I (Fig 3 7) |
1 | 2700-2703 | , there is more than
one value of V for the same current I (Fig 3 7) A material exhibiting
such behaviour is GaAs |
1 | 2701-2704 | 3 7) A material exhibiting
such behaviour is GaAs Materials and devices not obeying Ohm’s law in the form of Eq |
1 | 2702-2705 | 7) A material exhibiting
such behaviour is GaAs Materials and devices not obeying Ohm’s law in the form of Eq (3 |
1 | 2703-2706 | A material exhibiting
such behaviour is GaAs Materials and devices not obeying Ohm’s law in the form of Eq (3 3)
are actually widely used in electronic circuits |
1 | 2704-2707 | Materials and devices not obeying Ohm’s law in the form of Eq (3 3)
are actually widely used in electronic circuits In this and a few
subsequent chapters, however, we will study the electrical currents in
materials that obey Ohm’s law |
1 | 2705-2708 | (3 3)
are actually widely used in electronic circuits In this and a few
subsequent chapters, however, we will study the electrical currents in
materials that obey Ohm’s law 3 |
1 | 2706-2709 | 3)
are actually widely used in electronic circuits In this and a few
subsequent chapters, however, we will study the electrical currents in
materials that obey Ohm’s law 3 7 RESISTIVITY OF VARIOUS MATERIALS
The materials are classified as conductors, semiconductors and insulators
depending on their resistivities, in an increasing order of their values |
1 | 2707-2710 | In this and a few
subsequent chapters, however, we will study the electrical currents in
materials that obey Ohm’s law 3 7 RESISTIVITY OF VARIOUS MATERIALS
The materials are classified as conductors, semiconductors and insulators
depending on their resistivities, in an increasing order of their values FIGURE 3 |
1 | 2708-2711 | 3 7 RESISTIVITY OF VARIOUS MATERIALS
The materials are classified as conductors, semiconductors and insulators
depending on their resistivities, in an increasing order of their values FIGURE 3 5 The dashed line
represents the linear Ohm’s
law |
1 | 2709-2712 | 7 RESISTIVITY OF VARIOUS MATERIALS
The materials are classified as conductors, semiconductors and insulators
depending on their resistivities, in an increasing order of their values FIGURE 3 5 The dashed line
represents the linear Ohm’s
law The solid line is the voltage
V versus current I for a good
conductor |
1 | 2710-2713 | FIGURE 3 5 The dashed line
represents the linear Ohm’s
law The solid line is the voltage
V versus current I for a good
conductor FIGURE 3 |
1 | 2711-2714 | 5 The dashed line
represents the linear Ohm’s
law The solid line is the voltage
V versus current I for a good
conductor FIGURE 3 6 Characteristic curve
of a diode |
1 | 2712-2715 | The solid line is the voltage
V versus current I for a good
conductor FIGURE 3 6 Characteristic curve
of a diode Note the different
scales for negative and positive
values of the voltage and current |
1 | 2713-2716 | FIGURE 3 6 Characteristic curve
of a diode Note the different
scales for negative and positive
values of the voltage and current FIGURE 3 |
1 | 2714-2717 | 6 Characteristic curve
of a diode Note the different
scales for negative and positive
values of the voltage and current FIGURE 3 7 Variation of current
versus voltage for GaAs |
1 | 2715-2718 | Note the different
scales for negative and positive
values of the voltage and current FIGURE 3 7 Variation of current
versus voltage for GaAs Rationalised 2023-24
Physics
90
Metals have low resistivities in the range of 10–8 Wm to 10–6 Wm |
1 | 2716-2719 | FIGURE 3 7 Variation of current
versus voltage for GaAs Rationalised 2023-24
Physics
90
Metals have low resistivities in the range of 10–8 Wm to 10–6 Wm At the
other end are insulators like ceramic, rubber and plastics having
resistivities 1018 times greater than metals or more |
1 | 2717-2720 | 7 Variation of current
versus voltage for GaAs Rationalised 2023-24
Physics
90
Metals have low resistivities in the range of 10–8 Wm to 10–6 Wm At the
other end are insulators like ceramic, rubber and plastics having
resistivities 1018 times greater than metals or more In between the two
are the semiconductors |
1 | 2718-2721 | Rationalised 2023-24
Physics
90
Metals have low resistivities in the range of 10–8 Wm to 10–6 Wm At the
other end are insulators like ceramic, rubber and plastics having
resistivities 1018 times greater than metals or more In between the two
are the semiconductors These, however, have resistivities
characteristically decreasing with a rise in temperature |
1 | 2719-2722 | At the
other end are insulators like ceramic, rubber and plastics having
resistivities 1018 times greater than metals or more In between the two
are the semiconductors These, however, have resistivities
characteristically decreasing with a rise in temperature The resistivities
of semiconductors can be decreased by adding small amount of suitable
impurities |
1 | 2720-2723 | In between the two
are the semiconductors These, however, have resistivities
characteristically decreasing with a rise in temperature The resistivities
of semiconductors can be decreased by adding small amount of suitable
impurities This last feature is exploited in use of semiconductors for
electronic devices |
1 | 2721-2724 | These, however, have resistivities
characteristically decreasing with a rise in temperature The resistivities
of semiconductors can be decreased by adding small amount of suitable
impurities This last feature is exploited in use of semiconductors for
electronic devices 3 |
1 | 2722-2725 | The resistivities
of semiconductors can be decreased by adding small amount of suitable
impurities This last feature is exploited in use of semiconductors for
electronic devices 3 8
TEMPERATURE DEPENDENCE OF RESISTIVITY
The resistivity of a material is found to be dependent on the temperature |
1 | 2723-2726 | This last feature is exploited in use of semiconductors for
electronic devices 3 8
TEMPERATURE DEPENDENCE OF RESISTIVITY
The resistivity of a material is found to be dependent on the temperature Different materials do not exhibit the same dependence on temperatures |
1 | 2724-2727 | 3 8
TEMPERATURE DEPENDENCE OF RESISTIVITY
The resistivity of a material is found to be dependent on the temperature Different materials do not exhibit the same dependence on temperatures Over a limited range of temperatures, that is not too large, the resistivity
of a metallic conductor is approximately given by,
rT = r0 [1 + a (T–T0)]
(3 |
1 | 2725-2728 | 8
TEMPERATURE DEPENDENCE OF RESISTIVITY
The resistivity of a material is found to be dependent on the temperature Different materials do not exhibit the same dependence on temperatures Over a limited range of temperatures, that is not too large, the resistivity
of a metallic conductor is approximately given by,
rT = r0 [1 + a (T–T0)]
(3 26)
where rT is the resistivity at a temperature T and r0 is the same at a
reference temperature T0 |
1 | 2726-2729 | Different materials do not exhibit the same dependence on temperatures Over a limited range of temperatures, that is not too large, the resistivity
of a metallic conductor is approximately given by,
rT = r0 [1 + a (T–T0)]
(3 26)
where rT is the resistivity at a temperature T and r0 is the same at a
reference temperature T0 a is called the temperature co-efficient of
resistivity, and from Eq |
1 | 2727-2730 | Over a limited range of temperatures, that is not too large, the resistivity
of a metallic conductor is approximately given by,
rT = r0 [1 + a (T–T0)]
(3 26)
where rT is the resistivity at a temperature T and r0 is the same at a
reference temperature T0 a is called the temperature co-efficient of
resistivity, and from Eq (3 |
1 | 2728-2731 | 26)
where rT is the resistivity at a temperature T and r0 is the same at a
reference temperature T0 a is called the temperature co-efficient of
resistivity, and from Eq (3 26), the dimension of a is (Temperature)–1 |
1 | 2729-2732 | a is called the temperature co-efficient of
resistivity, and from Eq (3 26), the dimension of a is (Temperature)–1 For metals, a is positive |
1 | 2730-2733 | (3 26), the dimension of a is (Temperature)–1 For metals, a is positive The relation of Eq |
1 | 2731-2734 | 26), the dimension of a is (Temperature)–1 For metals, a is positive The relation of Eq (3 |
1 | 2732-2735 | For metals, a is positive The relation of Eq (3 26) implies that a graph of rT plotted against T
would be a straight line |
1 | 2733-2736 | The relation of Eq (3 26) implies that a graph of rT plotted against T
would be a straight line At temperatures much lower than 0°C, the graph,
however, deviates considerably from a straight line (Fig |
1 | 2734-2737 | (3 26) implies that a graph of rT plotted against T
would be a straight line At temperatures much lower than 0°C, the graph,
however, deviates considerably from a straight line (Fig 3 |
1 | 2735-2738 | 26) implies that a graph of rT plotted against T
would be a straight line At temperatures much lower than 0°C, the graph,
however, deviates considerably from a straight line (Fig 3 8) |
1 | 2736-2739 | At temperatures much lower than 0°C, the graph,
however, deviates considerably from a straight line (Fig 3 8) Equation (3 |
1 | 2737-2740 | 3 8) Equation (3 26) thus, can be used approximately over a limited range
of T around any reference temperature T0, where the graph can be
approximated as a straight line |
1 | 2738-2741 | 8) Equation (3 26) thus, can be used approximately over a limited range
of T around any reference temperature T0, where the graph can be
approximated as a straight line FIGURE 3 |
1 | 2739-2742 | Equation (3 26) thus, can be used approximately over a limited range
of T around any reference temperature T0, where the graph can be
approximated as a straight line FIGURE 3 8
Resistivity rT of
copper as a function
of temperature T |
1 | 2740-2743 | 26) thus, can be used approximately over a limited range
of T around any reference temperature T0, where the graph can be
approximated as a straight line FIGURE 3 8
Resistivity rT of
copper as a function
of temperature T FIGURE 3 |
1 | 2741-2744 | FIGURE 3 8
Resistivity rT of
copper as a function
of temperature T FIGURE 3 9 Resistivity
rT of nichrome as a
function of absolute
temperature T |
1 | 2742-2745 | 8
Resistivity rT of
copper as a function
of temperature T FIGURE 3 9 Resistivity
rT of nichrome as a
function of absolute
temperature T FIGURE 3 |
1 | 2743-2746 | FIGURE 3 9 Resistivity
rT of nichrome as a
function of absolute
temperature T FIGURE 3 10
Temperature dependence
of resistivity for a typical
semiconductor |
1 | 2744-2747 | 9 Resistivity
rT of nichrome as a
function of absolute
temperature T FIGURE 3 10
Temperature dependence
of resistivity for a typical
semiconductor
Some materials like Nichrome (which is an alloy of nickel, iron and
chromium) exhibit a very weak dependence of resistivity with temperature
(Fig |
1 | 2745-2748 | FIGURE 3 10
Temperature dependence
of resistivity for a typical
semiconductor
Some materials like Nichrome (which is an alloy of nickel, iron and
chromium) exhibit a very weak dependence of resistivity with temperature
(Fig 3 |
1 | 2746-2749 | 10
Temperature dependence
of resistivity for a typical
semiconductor
Some materials like Nichrome (which is an alloy of nickel, iron and
chromium) exhibit a very weak dependence of resistivity with temperature
(Fig 3 9) |
1 | 2747-2750 |
Some materials like Nichrome (which is an alloy of nickel, iron and
chromium) exhibit a very weak dependence of resistivity with temperature
(Fig 3 9) Manganin and constantan have similar properties |
1 | 2748-2751 | 3 9) Manganin and constantan have similar properties These
materials are thus widely used in wire bound standard resistors since
their resistance values would change very little with temperatures |
1 | 2749-2752 | 9) Manganin and constantan have similar properties These
materials are thus widely used in wire bound standard resistors since
their resistance values would change very little with temperatures Rationalised 2023-24
Current
Electricity
91
EXAMPLE 3 |
1 | 2750-2753 | Manganin and constantan have similar properties These
materials are thus widely used in wire bound standard resistors since
their resistance values would change very little with temperatures Rationalised 2023-24
Current
Electricity
91
EXAMPLE 3 3
Unlike metals, the resistivities of semiconductors decrease with
increasing temperatures |
1 | 2751-2754 | These
materials are thus widely used in wire bound standard resistors since
their resistance values would change very little with temperatures Rationalised 2023-24
Current
Electricity
91
EXAMPLE 3 3
Unlike metals, the resistivities of semiconductors decrease with
increasing temperatures A typical dependence is shown in Fig |
1 | 2752-2755 | Rationalised 2023-24
Current
Electricity
91
EXAMPLE 3 3
Unlike metals, the resistivities of semiconductors decrease with
increasing temperatures A typical dependence is shown in Fig 3 |
1 | 2753-2756 | 3
Unlike metals, the resistivities of semiconductors decrease with
increasing temperatures A typical dependence is shown in Fig 3 10 |
1 | 2754-2757 | A typical dependence is shown in Fig 3 10 We can qualitatively understand the temperature dependence of
resistivity, in the light of our derivation of Eq |
1 | 2755-2758 | 3 10 We can qualitatively understand the temperature dependence of
resistivity, in the light of our derivation of Eq (3 |
1 | 2756-2759 | 10 We can qualitatively understand the temperature dependence of
resistivity, in the light of our derivation of Eq (3 23) |
1 | 2757-2760 | We can qualitatively understand the temperature dependence of
resistivity, in the light of our derivation of Eq (3 23) From this equation,
resistivity of a material is given by
2
1
m
n e
ρ
σ
τ
=
=
(3 |
1 | 2758-2761 | (3 23) From this equation,
resistivity of a material is given by
2
1
m
n e
ρ
σ
τ
=
=
(3 27)
r thus depends inversely both on the number n of free electrons per unit
volume and on the average time t between collisions |
1 | 2759-2762 | 23) From this equation,
resistivity of a material is given by
2
1
m
n e
ρ
σ
τ
=
=
(3 27)
r thus depends inversely both on the number n of free electrons per unit
volume and on the average time t between collisions As we increase
temperature, average speed of the electrons, which act as the carriers of
current, increases resulting in more frequent collisions |
1 | 2760-2763 | From this equation,
resistivity of a material is given by
2
1
m
n e
ρ
σ
τ
=
=
(3 27)
r thus depends inversely both on the number n of free electrons per unit
volume and on the average time t between collisions As we increase
temperature, average speed of the electrons, which act as the carriers of
current, increases resulting in more frequent collisions The average time
of collisions t, thus decreases with temperature |
1 | 2761-2764 | 27)
r thus depends inversely both on the number n of free electrons per unit
volume and on the average time t between collisions As we increase
temperature, average speed of the electrons, which act as the carriers of
current, increases resulting in more frequent collisions The average time
of collisions t, thus decreases with temperature In a metal, n is not dependent on temperature to any appreciable
extent and thus the decrease in the value of t with rise in temperature
causes r to increase as we have observed |
1 | 2762-2765 | As we increase
temperature, average speed of the electrons, which act as the carriers of
current, increases resulting in more frequent collisions The average time
of collisions t, thus decreases with temperature In a metal, n is not dependent on temperature to any appreciable
extent and thus the decrease in the value of t with rise in temperature
causes r to increase as we have observed For insulators and semiconductors, however, n increases with
temperature |
1 | 2763-2766 | The average time
of collisions t, thus decreases with temperature In a metal, n is not dependent on temperature to any appreciable
extent and thus the decrease in the value of t with rise in temperature
causes r to increase as we have observed For insulators and semiconductors, however, n increases with
temperature This increase more than compensates any decrease in t in
Eq |
1 | 2764-2767 | In a metal, n is not dependent on temperature to any appreciable
extent and thus the decrease in the value of t with rise in temperature
causes r to increase as we have observed For insulators and semiconductors, however, n increases with
temperature This increase more than compensates any decrease in t in
Eq (3 |
1 | 2765-2768 | For insulators and semiconductors, however, n increases with
temperature This increase more than compensates any decrease in t in
Eq (3 23) so that for such materials, r decreases with temperature |
1 | 2766-2769 | This increase more than compensates any decrease in t in
Eq (3 23) so that for such materials, r decreases with temperature Example 3 |
1 | 2767-2770 | (3 23) so that for such materials, r decreases with temperature Example 3 3 An electric toaster uses nichrome for its heating
element |
1 | 2768-2771 | 23) so that for such materials, r decreases with temperature Example 3 3 An electric toaster uses nichrome for its heating
element When a negligibly small current passes through it, its
resistance at room temperature (27 |
1 | 2769-2772 | Example 3 3 An electric toaster uses nichrome for its heating
element When a negligibly small current passes through it, its
resistance at room temperature (27 0 °C) is found to be 75 |
1 | 2770-2773 | 3 An electric toaster uses nichrome for its heating
element When a negligibly small current passes through it, its
resistance at room temperature (27 0 °C) is found to be 75 3 W |
1 | 2771-2774 | When a negligibly small current passes through it, its
resistance at room temperature (27 0 °C) is found to be 75 3 W When
the toaster is connected to a 230 V supply, the current settles, after
a few seconds, to a steady value of 2 |
1 | 2772-2775 | 0 °C) is found to be 75 3 W When
the toaster is connected to a 230 V supply, the current settles, after
a few seconds, to a steady value of 2 68 A |
1 | 2773-2776 | 3 W When
the toaster is connected to a 230 V supply, the current settles, after
a few seconds, to a steady value of 2 68 A What is the steady
temperature of the nichrome element |
1 | 2774-2777 | When
the toaster is connected to a 230 V supply, the current settles, after
a few seconds, to a steady value of 2 68 A What is the steady
temperature of the nichrome element The temperature coefficient
of resistance of nichrome averaged over the temperature range
involved, is 1 |
1 | 2775-2778 | 68 A What is the steady
temperature of the nichrome element The temperature coefficient
of resistance of nichrome averaged over the temperature range
involved, is 1 70 × 10–4 °C–1 |
1 | 2776-2779 | What is the steady
temperature of the nichrome element The temperature coefficient
of resistance of nichrome averaged over the temperature range
involved, is 1 70 × 10–4 °C–1 Solution When the current through the element is very small, heating
effects can be ignored and the temperature T1 of the element is the
same as room temperature |
1 | 2777-2780 | The temperature coefficient
of resistance of nichrome averaged over the temperature range
involved, is 1 70 × 10–4 °C–1 Solution When the current through the element is very small, heating
effects can be ignored and the temperature T1 of the element is the
same as room temperature When the toaster is connected to the
supply, its initial current will be slightly higher than its steady value
of 2 |
1 | 2778-2781 | 70 × 10–4 °C–1 Solution When the current through the element is very small, heating
effects can be ignored and the temperature T1 of the element is the
same as room temperature When the toaster is connected to the
supply, its initial current will be slightly higher than its steady value
of 2 68 A |
1 | 2779-2782 | Solution When the current through the element is very small, heating
effects can be ignored and the temperature T1 of the element is the
same as room temperature When the toaster is connected to the
supply, its initial current will be slightly higher than its steady value
of 2 68 A But due to heating effect of the current, the temperature
will rise |
1 | 2780-2783 | When the toaster is connected to the
supply, its initial current will be slightly higher than its steady value
of 2 68 A But due to heating effect of the current, the temperature
will rise This will cause an increase in resistance and a slight
decrease in current |
1 | 2781-2784 | 68 A But due to heating effect of the current, the temperature
will rise This will cause an increase in resistance and a slight
decrease in current In a few seconds, a steady state will be reached
when temperature will rise no further, and both the resistance of the
element and the current drawn will achieve steady values |
1 | 2782-2785 | But due to heating effect of the current, the temperature
will rise This will cause an increase in resistance and a slight
decrease in current In a few seconds, a steady state will be reached
when temperature will rise no further, and both the resistance of the
element and the current drawn will achieve steady values The
resistance R2 at the steady temperature T2 is
R2
230 V
85 |
1 | 2783-2786 | This will cause an increase in resistance and a slight
decrease in current In a few seconds, a steady state will be reached
when temperature will rise no further, and both the resistance of the
element and the current drawn will achieve steady values The
resistance R2 at the steady temperature T2 is
R2
230 V
85 8
=2 |
1 | 2784-2787 | In a few seconds, a steady state will be reached
when temperature will rise no further, and both the resistance of the
element and the current drawn will achieve steady values The
resistance R2 at the steady temperature T2 is
R2
230 V
85 8
=2 68 A
=
Ω
Using the relation
R2 = R1 [1 + a (T2 – T1)]
with a = 1 |
1 | 2785-2788 | The
resistance R2 at the steady temperature T2 is
R2
230 V
85 8
=2 68 A
=
Ω
Using the relation
R2 = R1 [1 + a (T2 – T1)]
with a = 1 70 × 10–4 °C–1, we get
T2 – T1
–4
(85 |
1 | 2786-2789 | 8
=2 68 A
=
Ω
Using the relation
R2 = R1 [1 + a (T2 – T1)]
with a = 1 70 × 10–4 °C–1, we get
T2 – T1
–4
(85 8 – 75 |
1 | 2787-2790 | 68 A
=
Ω
Using the relation
R2 = R1 [1 + a (T2 – T1)]
with a = 1 70 × 10–4 °C–1, we get
T2 – T1
–4
(85 8 – 75 3)
=(75 |
1 | 2788-2791 | 70 × 10–4 °C–1, we get
T2 – T1
–4
(85 8 – 75 3)
=(75 3) 1 |
1 | 2789-2792 | 8 – 75 3)
=(75 3) 1 70 10
×
×
= 820 °C
that is, T2 = (820 + 27 |
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