Q48 / 54 · JEE Advanced 2019 (Paper 1) · Physics

In the circuit shown, initially there is no charge on capacitors and keys S1 and S2 are open. The values of the capacitors are C1=10 μF, C2=30 μF and C3= C4=80 μF.
Figure
Which of the statement(s) is/are correct?

  • A
    If key S1 is kept closed for long time such that capacitors are fully charged, the voltage difference between points P and Q will be 10 V.
  • B
    The keys S1 is kept closed for long time such that capacitors are fully charged. Now key S2 is closed, at this time, the instantaneous current across 30 Ω resistor (between points P and Q ) will be 0.2 A (round off to 1st decimal place).
  • Correct answer
    C
    At time t=0, the key S1 is closed, the instantaneous current in the closed circuit will be 25 mA.
  • Correct answer
    D
    If key S1 is kept closed for long time such that capacitors are fully charged, the voltage across the capacitors C1 will be 4V.

Solution

For option (C) , refer circuit diagram below
Figure
Just after closing of switch charge on all the capacitors C1, C3 and C4=0
∴ Replace all capacitors with wire, then circuit will get reduced as shown below.
Figure
i=570+100+30=5200=25 mA⇒(C) is correct
Now S1 is kept closed for long time circuit is in steady state
Figure
⇒ Apply KVL in loop, start from battery
+5-280-210-280=0
⇒10.280=5
⇒2=40 μC
⇒ Potential difference across C1
ΔVC1=210=4010=4 volt
⇒(D) is correct.
For option (B)⇒ Now just after closing of S2 charge on each capacitor remain same,
Refer circuit below -
Figure
KVL in left loop, starting from battery of 10 volts,
10-30x-4010-70y=0
⇒30x+70y=6 ...(i)
Now, apply KVL in right loop starting from 80 μF capacitor
⇒-4080+5+x-y30-4080+x-y×100-10+x×30=0
⇒160x-130y-6=0 ...(ii)
Now, solving equation (i) and (ii) we get,
y=961510
and x=0.05 amp. ⇒(B) is incorrect.

Hence, the correct answer is options: 'C', 'D'.

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