You take a couple of capacitors and connect them in series, to which you observe a total capacitance of 4.8microfarads. However, when you connect them in parallel their combined capacitance is 35microfarads. Determine the value of each capacitor.

C₁ = 34.8 μF

C₂ = 0.2 μF

Explanation:

When the capacitors are connected in series their resultant capacitance is given by the formula:

Cs = 1/C₁ + 1/C₂

where,

Cs = Series equivalent capacitance = 4.8 μF

C₁ = Capacitance of 1st Capacitor

C₂ = Capacitance of 2nd Capacitor

Therefore,

4.8 μF = 1/C₁ + 1/C₂

(4.8 μF)(C₁ C₂) = C₁ + C₂   equation 1

When the capacitors are connected in parallel their resultant capacitance is given by the formula:

Cp = C₁ + C₂

where,

Cp = Parallel equivalent capacitance = 35 μF

Therefore,

35 μF = C₁ + C₂   equation 2

solving equation 1 and equation 2 simultaneously, we get:

C₁ = 34.8 μF

C₂ = 0.2 μF

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