Question

An ac circuit consists of a voltage source
v=200sin120πt
and a
6μF
capacitor in series. Calculate the current established in the circuit

Answer 1

Answer on Question #45718 – Physics – Electromagnetism

Question: an AC circuit consists of a voltage source $V(t) = 200 \cdot \sin(120\pi t)$ and a $6\,\mu\mathrm{F}$ capacitor in series. Calculate the current established in the circuit.

Solution: charge, carried by the capacitor at some moment of time is

$$q = C V.$$

Thus, the current established in the circuit is

$$I = \frac{dq}{dt} = C \frac{dV}{dt}$$

Therefore,

$$I(t) = 200 \cdot 120\pi \cdot 6 \cdot 10^{-6} \cdot \cos(120\pi t) = 0,144\pi \cdot \cos(120\pi t).$$

Answer:

$$I(t) = 0,144\pi \cdot \cos(120\pi t).$$

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