3.20 EXERCISES

Q3.1 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?

A3.1 30 A

Q3.2 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?

A3.2 17 Ω, 8.5 V

Q3.3
(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.

A3.3


(a) 6 Ω


(b) 2 V, 4 V, 6 V

Q3.4


(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.

A3.4


(a) (20/19) Ω


(b) 10A, 5 A, 4A; 19A

Q3.5 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.

A3.5 1027 °C

Q3.6 A negligibly small current is passed through a wire of length 15 m and uniform cross-section 6.0 × 10^−7 m^2, and its resistance is measured to be 5.0 Ω. What is the resistivity of the material at the temperature of the experiment?

A3.6 2.0 × 10^−7 Ω m

Q3.7 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.

A3.7 0.0039 °C^−1

Q3.8 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.

A3.8 867 °C

Q3.9 Determine the current in each branch of the network shown in Fig. 3.30:

Fig. 3.30

A3.9 Current in branch AB = (4/17) A,


in BC = (6/17) A, in CD = (−4/17) A,


in AD = (6/17) A, in BD. = (−2/17) A, total current = (10/17) A.

Q3.10


(a) In a metre bridge [Fig. 3.27], 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?

A3.10 (a) X = 8.2 Ω; to minimise resistance of the connection which are not accounted for in the bridge formula.


(b) 60.5 cm from A.


(c) The galvanometer will show no current.

Q3.11 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?

A3.11 11.5 V; the series resistor limits the current drawn from the external source. In its absence, the current will be dangerously high.

Q3.12 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 63.0 cm, what is the EMF of the second cell?

A3.12 2.25 V

Q3.13 The number density of free electrons in a copper conductor estimated in Example 3.1 is 8.5 × 10^28 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 m^2 and it is carrying a current of 3.0 A.

A3.13 2.7 × 10^4 s (7.5 h)