Question

# A $3.0-\mathrm{M} \Omega$ resistor is connected in series with an initially uncharged $0.28-\mu \mathrm{F}$ capacitor. This arrangement is then connected across four 1.5-V batteries (also in series). (a) What is the maximum current in the circuit and when does it occur? (b) What percentage of the maximum current is in the circuit after 4.0 s? (c) What is the maximum charge on the capacitor and when does it occur? (d) What percentage of the maximum charge is on the capacitor after 4.0 s? (e) How much energy is stored in the capacitor after one time constant has elapsed?

Solution

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Given:

• Resistance: $R = 3 \mathrm{~M \Omega}$;
• Capacitance: $C = 0.28 \mathrm{~\mu F }$;
• Voltage: $V_1 = 1.5 \mathrm{~V}$;
• Number of batteries: $n= 4$;
• Time: $t_1 = 4 \mathrm{~s}$;
• Time: $t_2 = \tau$;

Required: a) The largest possible current in the circuit $I$; b) Ratio of the currents $\frac{I_1}{I}$; c) The largest amount of the charge $Q$; d) Ratio of the charges $\frac{Q_1}{Q}$; e) The amount of stored energy $U$;

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