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In the given circuit diagram figure, swi...

In the given circuit diagram figure, switch `S_w` is shifted from position 1 to position 2. Then

A

a charge of amount `CE_2` will be supplied to battery `E_1`.

B

heat generated in the circuit is `CE_(2)^(2)//2`

C

a charge of amount `CE_2` will be supplied by battery `E_1`.

D

heat generated in the circuit is `CE_1E_2//2`

Text Solution

Verified by Experts

The correct Answer is:
B
b. Initially, when the switch is closed on position 1, the capacitor
C is connected in series with batteries `E_1 and E_2`. Fr4om KVL,
we have
`Q_i/C - E_2 + E_1 = 0`
or `Q_i = (E_2-E_1)C`………(i)
Depending upon the sigh of `(E_2-E_1)`, charge `Q_i` on the left plate may be positive (if `E_2gtE_1`), or negative `(if E_2ltE_1)`, charge on right plate would be equal and opposite. When the
switch is moved to position 2, the left plate (earlier having
charge `+Q_i`) will now have charge
`Q_(f) = E_1C` .......(ii)
The net charge flow through the circuit is
`Delta Q = Q_(f) - Q_(i) = [-E_1-(E_2-E_1)]C = -E_2C`
We can say that a net positive charge equal to E_2C is pulled
by the battery of emf `E_1` from the left plate of the capacitor,
which flows through battery `E_1` and is transferred to the right plate of the capacitor. Work done by battery `E_1` in the process of charge transfer is
`Delta W = E_1E_2C`
and the remaining part is lost as joule heat:
` H = DeltaW - DeltaW_C = 1/2 E_(2)^(2)C`.
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