An uncharged 30.0-µF capacitor is connected in series with a 25.0-Ω resistor, a DC battery, and an open switch. The battery has an internal resistance of 10.0 Ω and the open-circuit voltage across its terminals is 50.0 V. The leads have no appreciable resistance. At time t = 0, the switch is suddenly closed.

(a) What is the maximum current through the 25.0-Ω resistor?
(c) What is the maximum charge that the capacitor receives?

(a) Maximum current through resistor is 1.43 A

(b) Maximum charge capacitor receives is .

Explanation:

(a)

In an RC (resistor-capacitor) DC circuit, when charging, the current at any time, t, is given by

Here, is the maximum current and τ represents time constant which is given by RC (the product of the resistance and capacitance).

The maximum current is given by

V is the emf of the battery and is the effective resistance.

In this question, = 10.0 Ω + 25.0 Ω = 35.0 Ω

(b) The maximum charge is given

Q = CV

where C is the capacitance of the capacitor

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