Three capacitors C 1 , C 2 and C 3 are connected to voltage source V as shown in figure. The voltage across C 3 will be

Question

Three capacitors C 1 ​ , C 2 ​ and C 3 ​ are connected to voltage source V as shown in figure. The voltage across C 3 ​ will be

TestHub · Accepted Answer

From the given circuit diagram, capacitors $C_{1}$ and $C_{2}$ are connected in parallel.

Their equivalent capacitance is $C_{12} = C_{1} + C_{2}$ .

This equivalent capacitor $C_{12}$ is connected in series with capacitor $C_{3}$ .

In a series combination, the charge $Q$ on each capacitor is the same. The total equivalent capacitance of the circuit is:

$C_{e q} = \frac{C _{12} C _{3}}{C _{12} + C _{3}} = \frac{( C _{1} + C _{2} ) C _{3}}{C _{1} + C _{2} + C _{3}}$

The total charge supplied by the voltage source is:

$Q = C_{e q} V = \frac{( C _{1} + C _{2} ) C _{3} V}{C _{1} + C _{2} + C _{3}}$

The voltage across $C_{3}$ is given by:

$V_{3} = \frac{Q}{C _{3}} = \frac{1}{C _{3}} \times \frac{( C _{1} + C _{2} ) C _{3} V}{C _{1} + C _{2} + C _{3}} = \frac{( C _{1} + C _{2} ) V}{C _{1} + C _{2} + C _{3}}$

Answer: $\frac{( C _{1} + C _{2} ) V}{( C _{1} + C _{2} + C _{3} )}$

Physics - Capacitor Question with Solution | TestHub

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