SATHEE: Electrostatics Question 582

Electrostatics Question 582

Question: Two condensers $C_{1}$ and $C_{2}$ in a circuit are joined . The potential of point $A$ is $V_{1}$ and that of $B$ is $V_{2}$ . The potential of point $D$ will be [MP PMT 1997]

Options:

A) $\frac{1}{2} (V_{1} + V_{2})$

B) $\frac{C_{2} V_{1} + C_{1} V_{2}}{C_{1} + C_{2}}$

C) $\frac{C_{1} V_{1} + C_{2} V_{2}}{C_{1} + C_{2}}$

D) $\frac{C_{2} V_{1} - C_{1} V_{2}}{C_{1} + C_{2}}$

Show Answer

Answer:

Correct Answer: C

Solution:

Charge on $C_{1}$ = charge on $C_{2}$

therefore $C_{1} (V_{A} - V_{D}) = C_{2} (V_{D} - V_{B})$

therefore $C_{1} (V_{1} - V_{D}) = C_{2} (V_{D} - V_{2})$

therefore $V_{D} = \frac{C_{1} V_{1} + C_{2} V_{2}}{C_{1} + C_{2}}$

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