NCERT Solutions Class 12 Physics Chapter 3 Current Electricity Download In Pdf

Chapter 3 Current Electricity Download in pdf

**Question 3.1** The storage battery of a car has an emf of 12 V. If the internal
resistance of the battery is 0.4 Ω, what is the maximum current
that can be drawn from the battery?

**Question 3.2** A battery of emf 10 V and internal resistance 3 Ω is connected to a
resistor. If the current in the circuit is 0.5 A, what is the resistance
of the resistor? What is the terminal voltage of the battery when the
circuit is closed?

**Question 3.3** (a) Three resistors 1 Ω, 2 Ω, and 3 Ω are combined in series. What
is the total resistance of the combination? (b) If the combination is connected to a battery of emf 12 V and
negligible internal resistance, obtain the potential drop across
each resistor.

**Question 3.4** (a) Three resistors 2 Ω, 4 Ω and 5 Ω are combined in parallel. What
is the total resistance of the combination?

(b) If the combination is connected to a battery of emf 20 V and
negligible internal resistance, determine the current through
each resistor, and the total current drawn from the battery.

**Question 3.5** At room temperature (27.0 °C) the resistance of a heating element
is 100 Ω. What is the temperature of the element if the resistance is
found to be 117 Ω, given that the temperature coefficient of the
material of the resistor is 1.70 × 10–4 °C–1.

**Question 3.6** A negligibly small current is passed through a wire of length 15 m
and uniform cross-section 6.0 × 10–7 m2, and its resistance is
measured to be 5.0 Ω. What is the resistivity of the material at the
temperature of the experiment?

**Question 3.7** A silver wire has a resistance of 2.1 Ω at 27.5 °C, and a resistance
of 2.7 Ω at 100 °C. Determine the temperature coefficient of
resistivity of silver.

**Question 3.8** A heating element using nichrome connected to a 230 V supply
draws an initial current of 3.2 A which settles after a few seconds to a steady value of 2.8 A. What is the steady temperature of the heating
element if the room temperature is 27.0 °C? Temperature coefficient
of resistance of nichrome averaged over the temperature range
involved is 1.70 × 10–4 °C–1.

**Question 3.9** Determine the current in each branch of the network shown in
Fig. 3.30:

**Question 3.10** (a) In a metre bridge [Fig. 3.7], the balance point is found to be at
39.5 cm from the end A, when the resistor Y is of 12.5 Ω.
Determine the resistance of X. Why are the connections between
resistors in a Wheatstone or meter bridge made of thick copper
strips?

(b) Determine the balance point of the bridge above if X and Y are
interchanged.

(c) What happens if the galvanometer and cell are interchanged at
the balance point of the bridge? Would the galvanometer show
any current?

**Question 3.11** A storage battery of emf 8.0 V and internal resistance 0.5 Ω is being
charged by a 120 V dc supply using a series resistor of 15.5 Ω. What
is the terminal voltage of the battery during charging? What is the
purpose of having a series resistor in the charging circuit?

**Question 3.12** In a potentiometer arrangement, a cell of emf 1.25 V gives a balance
point at 35.0 cm length of the wire. If the cell is replaced by another
cell and the balance point shifts to 6 3.0 cm, what is the emf of the
second cell?

**Question 3. 13** The number density of free electrons in a copper conductor
estimated in Example 3.1 is 8.5 × 1028 m–3. How long does an electron
take to drift from one end of a wire 3.0 m long to its other end? The
area of cross-section of the wire is 2.0 × 10–6 m2 and it is carrying a
current of 3.0 A.

ADDITIONAL EXERCISES QUESTIONS

**Question 3. 14** The earth’s surface has a negative surface charge density of 10–9 C
m–2. The potential difference of 400 kV between the top of the
atmosphere and the surface results (due to the low conductivity of
the lower atmosphere) in a current of only 1800 A over the entire
globe. If there were no mechanism of sustaining atmospheric electric field, how much time (roughly) would be required to neutralise the
earth’s surface? (This never happens in practice because there is a
mechanism to replenish electric charges, namely the continual
thunderstorms and lightning in different parts of the globe). (Radius
of earth = 6.37 × 106 m.)

**Question 3.15** (a) Six lead-acid type of secondary cells each of emf 2.0 V and internal
resistance 0.015 Ω are joined in series to provide a supply to a
resistance of 8.5 Ω. What are the current drawn from the supply
and its terminal voltage?

(b) A secondary cell after long use has an emf of 1.9 V and a large
internal resistance of 380 Ω. What maximum current can be drawn
from the cell? Could the cell drive the starting motor of a car?

**Question 3.16** Two wires of equal length, one of aluminium and the other of copper
have the same resistance. Which of the two wires is lighter? Hence
explain why aluminium wires are preferred for overhead power cables.
(ρAl = 2.63 × 10–8 Ω m, ρCu = 1.72 × 10–8 Ω m, Relative density of
Al = 2.7, of Cu = 8.9.)

**Question 3.17** What conclusion can you draw from the following observations on a
resistor made of alloy manganin?

**Question 3.18** Answer the following questions:

(a) A steady current flows in a metallic conductor of non-uniform
cross-section. Which of these quantities is constant along the
conductor: current, current density, electric field, drift speed?

(b) Is Ohm’s law universally applicable for all conducting elements?
If not, give examples of elements which do not obey Ohm’s law.

(c) A low voltage supply from which one needs high currents must
have very low internal resistance. Why?

(d) A high tension (HT) supply of, say, 6 kV must have a very large
internal resistance. Why?

**Question 3.19** Choose the correct alternative:

(a) Alloys of metals usually have (greater/less) resistivity than that
of their constituent metals.

(b) Alloys usually have much (lower/higher) temperature
coefficients of resistance than pure metals.

(c) The resistivity of the alloy manganin is nearly independent of/
increases rapidly with increase of temperature.

(d) The resistivity of a typical insulator (e.g., amber) is greater than
that of a metal by a factor of the order of (1022/103).

**Question 3.20** (a) Given n resistors each of resistance R, how will you combine
them to get the

(i) maximum

(ii) minimum effective resistance?
What is the ratio of the maximum to minimum resistance?
(b) Given the resistances of 1 Ω, 2 Ω, 3 Ω, how will be combine them
to get an equivalent resistance of (i) (11/3) Ω (ii) (11/5) Ω,

(iii) 6
Ω, (iv) (6/11) Ω?
(c) Determine the equivalent resistance of networks shown in
Fig. 3.31.

**Question 3.22** Figure 3.33 shows a potentiometer with a cell of 2.0 V and internal
resistance 0.40 Ω maintaining a potential drop across the resistor
wire AB. A standard cell which maintains a constant emf of 1.02 V
(for very moderate currents upto a few mA) gives a balance point at
67.3 cm length of the wire. To ensure very low currents drawn from
the standard cell, a very high resistance of 600 kΩ is put in series
with it, which is shorted close to the balance point. The standard
cell is then replaced by a cell of unknown emf ε and the balance
point found similarly, turns out to be at 82.3 cm length of the wire.

(c) Is the balance point affected by this high resistance?

(d) Is the balance point affected by the internal resistance of the
driver cell?

(e) Would the method work in the above situation if the driver cell
of the potentiometer had an emf of 1.0V instead of 2.0V?
(f ) Would the circuit work well for determining an extremely small
emf, say of the order of a few mV (such as the typical emf of a
thermo-couple)? If not, how will you modify the circuit?

**Question 3.23** Figure 3.34 shows a potentiometer circuit for comparison of two
resistances. The balance point with a standard resistor R = 10.0 Ω
is found to be 58.3 cm, while that with the unknown resistance X is
68.5 cm. Determine the value of X. What might you do if you failed
to find a balance point with the given cell of emf ε ?

**Question 3.24 **Figure 3.35 shows a 2.0 V potentiometer used for the determination
of internal resistance of a 1.5 V cell. The balance point of the cell in
open circuit is 76.3 cm. When a resistor of 9.5 Ω is used in the external
circuit of the cell, the balance point shifts to 64.8 cm length of the
potentiometer wire. Determine the internal resistance of the cell.

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- Chapter 1 Electric Charges and Fields
- Chapter 2 Electrostatic Potential and Capacitance
- Chapter 3 Current Electricity
- Chapter 4 Moving Charges and Magnetism
- Chapter 5 Magnetism and Matter
- Chapter 6 Electromagnetic Induction
- Chapter 7 Alternating Current
- Chapter 8 Electromagnetic Waves
- Chapter 9 Ray Optics and Optical Instruments
- Chapter 10 Wave Optics
- Chapter 11 Dual Nature of Radiation and Matter
- Chapter 12 Atoms
- Chapter 13 Nuclei
- Chapter 14 Semiconductor Electronics: Materials, Devices and Simple Circuits
- Chapter 15 Communication Systems

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