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Study the information given and answer the questions that follow.
A 2 μF capacitor, 100 Ω resistor and 8 H inductor are connected in series with an ac source. At a…
A $2\ \mu\text{F}$ capacitor, $100\ \Omega$ resistor and $8\text{ H}$ inductor are connected in series with an ac source. At a certain frequency of about 40 Hz for this ac source, the current drawn in the circuit is maximum. If the peak value of e.m.f. of the source is 200V:
(i)[1]
What is the peak value of current in the circuit?
- (a)$1.4\text{ A}$
- (b)$2.2\text{ A}$
- (c)$2.0\text{ A}$
- (d)$1.8\text{ A}$
(ii)[1]
What is the phase relation between voltages across inductor and resistor?
- (a)$\pi/2\text{ radian}$
- (b)$\pi/3\text{ radian}$
- (c)$\pi/4\text{ radian}$
- (d)$\pi\text{ radian}$
(iii)[1]
What is the phase difference between voltages across inductor and capacitor?
- (a)$\pi/2\text{ radian}$
- (b)$\pi/3\text{ radian}$
- (c)$\pi/4\text{ radian}$
- (d)$\pi\text{ radian}$
Answer
Answer (i)
Correct option: (c)
Answer: (c) $2.0\text{ A}$
Current is maximum at resonance, where $Z = R$: $I_0 = \frac{200}{100} = 2.0\text{ A}$.
Answer (ii)
Correct option: (a)
Answer: (a) $\pi/2\text{ radian}$
Voltage across the inductor leads the current by $\frac{\pi}{2}$; voltage across the resistor is in phase with the current.
Answer (iii)
Correct option: (d)
Answer: (d) $\pi\text{ radian}$
Voltage across the inductor leads the current by $\frac{\pi}{2}$ and that across the capacitor lags by $\frac{\pi}{2}$, so they are in antiphase.