Introduction to Electric Circuits

8.6 Problems 203

2 The armature of a relay operates on a 200 V supply and is actuated when

the current through its coil is 240 mA. The relay is required to close 4 ms

after switching on the circuit. This time is also the time constant of the

circuit. Calculate (a) the resistance and inductance of the coil and (b) the

initial rate of rise of the current.

3 A series circuit consists of a resistor R (= 10 1~) in series with a coil having

an inductance of 2 H and a resistance of 10 1~. The circuit is fed from a

100 V d.c. supply and after it has been on for several minutes a short

circuit fault suddenly occurs across the resistor R. Determine (a) the

current in the circuit 0.1 s after the occurrence of the fault and (b) the time

taken for the current to reach its new steady state value.

4 A resistor is connected in series with a 2 ~F capacitor across a 200 V d.c.

supply. A neon lamp with a striking voltage of 120 V is connected across

the capacitor. Calculate the value of the resistance required to make the

lamp flash 5 s after switching the circuit on.

5 An imperfect capacitor of 10 ~F capacitance is fully charged from a 200 V

d.c. supply. After being disconnected from the supply the voltage across its

plates falls to 100 V in 20 s. Calculate the leakage resistance of the

capacitor.

6 A 2 ~F capacitor is connected in series with a 2 kl~ resistance to a 100 V

d.c. supply having an effective internal resistance of 2 kl-l. The supply is

switched on for 10 ms and then replaced by a short circuit. Determine the

total time for which the capacitor voltage is greater than 10 V. Sketch the

waveform of the voltage across the capacitor and of the current through it.

7 From the instant that the switch S in the circuit of Fig. 8.41 is closed, (a)

show that the current through the capacitor is given by

ic - (V/R1) exp [-R~ + Rz)t/CR1R2], (b) obtain numerical expressions for

the voltage across the capacitor and the current supplied by the source.

20v

o "---~ S

R2 ~ 20 k~

20k~

C

0.1 pF T

Figure 8.41

8 The RL integrator circuit shown in Fig. 8.9 has R = 47fl and L = 120 mH.

Obtain the output voltage (Vo) waveform when the input voltage V~, is:

(a) a step function of amplitude 20 V;