A 3.41 uF and a 7.26uF capacitor are connected in series across a 30.0-V battery

Question

A 3.41 uF and a 7.26uF capacitor are connected in series across a 30.0-V battery. A 7.98 uF capacitor is then connected in parallel across the 3.41uF capacitor. Determine the voltage across the 7.98uF capacitor. Thank you very much!

Hint:First find the equivalent capacitance of the complete arrangement as follows: (1) Sketch the arrangement of capacitors. (2) Find the equivalent capacitance of the parallel combination. (3) Find the equivalent capacitance of the resulting series combination. Next, calculate the charge on the equivalent capacitor using equation q=CV. This amount of charge resides on the single capacitor and this same amount of charge is shared between the two capacitors in parallel.

Explanation / Answer

Voltage = V = 30 V

3.41 uF and 7.26uF capacitor are in series

7.98 uF is parallel to 3.41 uF

Equivalrnt capacitance of parallel combination = 7.98 + 3.41 = 11.39 uF

Equivalent capacitance of the combination = C = 11.39 * 7.26 / ( 11.39 + 7.26 ) = 4.434 uF

Charge on the equivalent capacitor= q = C V = 4.434 x 30 = 133.02 uC

Charge on parallel combination is same = q = 133.02 uC

133.02 uC is distributed between 7.98 uF and 3.41 uF

Voltage across the 7.98 uF = q / 7.98 uF = 133.02 / 7.98 = 16.67 V

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