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**(1)** In the circuit shown, the battery and the inductor have negligible resistance. The currents through R_{1}, R_{2} and R_{3} are i_{1}, i_{2} and i_{3} respectively when the switch S is kept closed. The switch S is closed at time *t* = 0.

(a) Calculate the potential difference across the 8 Ω resistor R_{2 }immediately after closing the switch S.

(b) If the inductance is replaced by an uncharged 10 μF capacitor what will be the potential difference across the 8 Ω resistor R_{2} immediately after closing the switch S? Justify your answer.

(c) After reaching steady state, in case (b) what will be the potential difference across the resistor R_{2}? Justify your answer.

(d) If a 16 Ω resistor is used instead of the capacitor mentioned in (b), calculate the current through R_{2} immediately after closing the switch S.

(e) Show the nature of variation of the potential difference across R_{2} with time *t *in cases (b) and (d).

**(2) **In the above circuit, suppose the switch S was closed for sufficiently long time so that steady state was reached. In this steady state the switch S is *opened* at time *t* = 0.

(a) Will there be any change in the *directions* of the currents i_{2} and i_{3} on opening the switch S? Put a tick mark against the correct option among the following:

No change____

Current i_{2} alone is reversed____

Current i_{3} alone is reversed____

Both i_{2} and i_{3} are reversed____

Justify your answer.

(b) Calculate the potential difference across resistance R_{2} immediately after opening the switch S.

(c) Calculate the total amount of heat generated in resistance R_{2} after switch S is *opened*.

(d) Calculate the *power* dissipated in resistance R_{2} in the steady state, *before opening the switch S.*

Try to answer the above two questions which carry 15 points each. You can take about 15 minutes for answering each question.

I’ll be back shortly with model answers for your benefit.

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