Different Types of AC Circuits: AC Voltage Applied to a Series LCR Circuit

Two coils A and B have inductances 1.0 H and 2.0 H respectively. The resistance of each coil is 10 Ω. Each coil is connected to an ideal battery of emf 2.0 V at t = 0. Let i_A and i_Bbe the currents in the two circuit at time t. Find the ratio i_A / i_B at (a) t = 100 ms, (b) t = 200 ms and (c) t = 1 s.

A series LCR circuit containing 5.0 H inductor, 80 µF capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be ______.

Show that in an a.c. circuit containing a pure inductor, the voltage is ahead of current by π/2 in phase ?

Three students, X, Y and Z performed an experiment for studying the variation of ac with frequency in a series LCR circuit and obtained the graphs as shown below. They all used

• an AC source of the same emf and
• inductance of the same value.

1. Who used minimum resistance?
2. In which case will the quality Q factor be maximum?
3. What did the students conclude about the nature of impedance at resonant frequency (f₀)?
4. An ideal capacitor is connected across 220 V, 50 Hz, and 220 V, 100 Hz supplies. Find the ratio of current flowing through it in the two cases.

Consider the circuit shown in figure. (a) Find the current through the battery a long time after the switch S is closed. (b) Suppose the switch is again opened at t = 0. What is the time constant of the discharging circuit? (c) Find the current through the inductor after one time constant.

Keeping the source frequency equal to the resonating frequency of the series LCR circuit, if the three elements, L, C and R are arranged in parallel, show that the total current in the parallel LCR circuit is minimum at this frequency. Obtain the current rms value in each branch of the circuit for the elements and source specified for this frequency.

If the rms current in a 50 Hz ac circuit is 5 A, the value of the current 1/300 seconds after its value becomes zero is ______.