A 100 μF capacitor in series with a 40Ω resistance is connected to a 110 V, 60 Hz supply.

(a) What is the maximum current in the circuit?


(b) What is the time lag between the current maximum and the voltage maximum?

Given: capacitor C = 100 μf = 100 × 10-6F

Resistance R = 40Ω


Voltage V = 110 V


Frequency v = 60 Hz


(a) Angular frequency is given by the relation: ω = 2πv


ω = 2π × 60 rad/s


The impedance is given by the relation



Or Z2 =


Peak voltage is given by the relation V0 = V √2


Or V0 = 110 √ 2 V


The maximum current is given by the following relation:


I0 = V0/Z


I0 =


I0 =


On calculating, we get


I0 = 3.24 A


(b) Since in capacitor circuit, the voltage lags behind the current by a phase angle Ф. Therefore, the phase angle is given by the expression


tanФ =


tanФ = 1/ωCR


substituting the values, we get


tanФ = 1/(120π(rad/s) × 10-4(F) × 40 (Ω))


On calculating, we get


tanФ = 0.6635


or Ф = 33.56°


in radians, Ф = (33.56 π) /180


Time lag is given by the relation


t = Ф/ω


t =


on calculating, we get


t = 1.55 × 10-3s


on converting in ms, we get time lag t = 1.55 ms.


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