A capacitor of 10 μ F charged upto 250 V is connected in parallel with another capacitor of 5 μ F charged upto 100 V. The common potential is :

Question

A capacitor of 10 μ F charged upto 250 V is connected in parallel with another capacitor of 5 μ F charged upto 100 V. The common potential is : (A) 200 V (B) 300 V (C) 400 V (D) 500 V

Tardigrade Admin · Accepted Answer

The equivalent capacitance of the capacitors joined in parallel is equal to the sum of their individual capacitances.
Let the charge on the capacitor's be

q_{1}

and

q_{2}

. Then total charge is

Q = Q_{1} + Q_{2}

C V = C_{1} V_{1} + C_{2} V_{2}

Since, capacitor's are connected in parallel equivalent capacitance is

C = C_{1} + C_{2}

∴ V = \frac{C _{1} V _{1} + C _{2} V _{2}}{C _{1} + C _{2}}

Given,

C_{1} = 10 μ F,

V_{1} = 250 V,

C_{2} = 5 μ F,

V_{2} = 100 V

∴ V = \frac{( 10 \times 1 0 ^{- 6} \times 250 ) + ( 5 \times 1 0 ^{- 6} \times 100 )}{( 10 \times 1 0 ^{- 6} + 5 \times 1 0 ^{- 6} )}

\Rightarrow V = \frac{3000 \times 1 0 ^{- 6}}{15 \times 1 0 ^{- 6}}

= 200

volt

Q. A capacitor of 10μF charged upto 250V is connected in parallel with another capacitor of 5μF charged upto 100V. The common potential is :

200 V

300 V

400 V

500 V

Q. A capacitor of $10 μ F$ charged upto $250 V$ is connected in parallel with another capacitor of $5 μ F$ charged upto $100 V$ . The common potential is :