What would be the voltage across `C_(3)?`

Options

A. ` (( C _ 1 + C _ 2 ) V ) / ( C _ 1 + C _ 2 + C _ 3 ) `
B. ` ( C _ 1 V) /( C _ 1 + C _ 2 + C _ 3 ) `
C. ` ( C_ 2 V ) /( C _ 2 + C _ 2 + C _ 3 ) `
D. ` ( C _ 3 V ) /( C _ 1 + C _ 2 + C _ 3 )`

Answer

A

Explanation

Capacitors ` C _ 1 and C _ 2 ` are in parallel, their equivalent capacitance is in series with capacitor ` C _ 3`. Hence, the equvalent capacitance of the given circuit is
` C _ ( eq ) = ((C _ 1 + C _ 2 )C _ 3) /( C _ 1 + C _ 2 + C _ 3 ) `
Charge on capacitor ` C_ 3 ` is
` Q = V C _ ( eq ) `
` = ( V ( C _ 1 + C _ 2 ) C _ 3 ) / ( C _ 1 + C _ 2 + C _ 3 ) `
Voltage across ` C _ 3 ` is
` = (Q) / ( C _ 3 ) = ( V ( C _ 1 + C _ 2 ) ) / ( C_ 1 + C_ 2 + C _ 3 ) `