Question

Determine the potential difference across the plates of the capacitor C1 of the network shown in the figure. (Assume E2>E1

Answer 1

The potential difference is C2(E2−E1)/C1+C2

Applying Kirchhoff's voltage law in the loop clockwise

−E2 − q/C2 + E1 − qC1 =0

= q/C1+q/C2 = E2  −E1

= q( 1/C1 + 1/C2 ) = E2−E1

= q × ( C1+C2  /C1×C2) = E2 − E1

= q = (C1×C2)× (E2−E1)/C1+C2

Potential difference across C1 -

V1 = q/C1

= C2(E2−E1)/C1+C2

Therefore, the potential difference is C2(E2−E1)/C1+C2

Answer 2

The potential difference = [C2(E2−E1)] / [C1+C2]

Explanation:

Applying Kirchhoff's voltage law in the loop clockwise, we get:

- E2 - q/C2 + E1 - qC1 = 0

q/C1 + q/C2 = E2 - E1

q( 1/C1 + 1/C2 ) = E2 - E1

q [ (C1 + C2)  / (C1*C2) ] = E2 - E1

q = (C1*C2) * (E2 - E1) / (C1 +C2)

Potential difference across C1 is:

V1 = q/C1

= C2 (E2-E1) / (C1+C2)