In the given circuitthe potential difference Vx−Vy betw

In the given circuit,the potential difference $(V_{x} - V_{y})$ between the points $x$ and $y$ when capacitors reach steady state is___

$- 7 V$

$- 18 V$

$+ 18 V$

$+ 7 V$

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Given $E = 24 V, R = 2 Ω, R_{1} = 4 Ω, R_{2} = 6 Ω, C_{1} = (\frac{4}{3}) μ F, C_{2} = 4 μ F$ .

As the capacitor offers a very high resistance to the current in the steady state, Current through the branch having capacitors is zero.

Now, the total resistance in the circuit is

$R_{e q} = R + R_{1} + R_{2} = 2 + 4 + 6 = 12 Ω$

Hence, the net current in the circuit $= \frac{E}{R_{e q}} = \frac{24}{12} = 2 A$

Therefore, the terminal potential difference across is

$V_{A} - V_{B} = 24 - 2 \times 2 = 20 V$

$V_{A} - V_{y} = \frac{4 \times 20}{10} = + 8 V$

$V_{A} - V_{x} = \frac{4 \times 20}{4 \frac{4}{3}} = + 15 V$

$∴ V_{x} - V_{y} = - 7 V$