A circuit consists of a capacitor, a 24–V battery, and an ac voltage connected as shown in figure. The ac voltage is given by = (20 V) cos (120πt) where t is in seconds. Find the charge on capacitor as a function of time. Assume that transient effects have had sufficient time to decay.
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The circuit has a DC battery (24 V) and an AC source (20 V cos(120πt)) in parallel with a capacitor. The total voltage across the capacitor is the sum of the DC and AC components. The charge on a capacitor is given by Q = C * V. Therefore, the total charge is Q(t) = C * [V_dc + V_ac(t)] = C * [24 + 20 cos(120πt)].
This corresponds to the expression:
Final Answer: Option 1