A capacitor that is initially uncharged is connected in...

A capacitor that is initially uncharged is connected in series with a resistor and an emf source with $\mathcal{E}=110 \mathrm{V}$ and negligible internal resistance. Just after the circuit is completed, the current through the resistor is $6.5 \times 10^{-5} \mathrm{A}$ . The time constant for the circuit is 6.2 $\mathrm{s}$ . What are the resistance of the resistor and the capacitance of the capacitor?

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Key Concepts

Time Constant

The time constant (?) of an RC circuit, defined as the product of resistance and capacitance (? = RC), is a crucial measure of how quickly the circuit responds. It characterizes the rate at which the capacitor charges or discharges, indicating the time required for the voltage or current to reach about 63% of its final value.

Ohm's Law

Ohm's Law relates the voltage, current, and resistance in a circuit. In an RC circuit, especially at the moment immediately after a switch is closed when the capacitor is uncharged, the capacitor behaves like a short circuit, making the initial current determination straightforward by dividing the applied voltage by the resistance.

RC Circuit Analysis

RC circuits, which consist of a resistor and a capacitor in series, are fundamental in studying transient responses. These circuits exhibit time-dependent charging and discharging behavior, and understanding their overall behavior is essential when analyzing the initial charging conditions and the evolution of voltage and current over time.

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