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

A capacitor that is initially uncharged is connected in series with a resistor and a 400.0 $\mathrm{V}$ emf source with negligible internal resistance. Just after the circuit is completed, the current through the resistor is 0.800 $\mathrm{mA}$ and the time constant for the circuit is 6.00 s. What are (a) the resistance of the resistor and (b) the capacitance of the capacitor?

Key Concepts

RC Time Constant

In an RC circuit, the time constant (?) is the product of the resistance (R) and the capacitance (C) of the circuit. It represents the time required for the capacitor to charge up to about 63.2% of the applied voltage or, conversely, to discharge to about 36.8% of its initial voltage. This concept is fundamental in defining the transient response of the circuit when a voltage is applied or removed.

Ohm's Law

Ohm's Law is a principle that relates the voltage (V), current (I), and resistance (R) in an electrical circuit using the formula V = I × R. In the context of an RC circuit, this law is used to determine the initial current at the moment the capacitor starts to charge, given that the capacitor initially behaves like a short circuit (i.e., it has zero voltage across it).

Capacitor Charging Behavior

When a capacitor is connected in series with a resistor to an emf source, the capacitor initially has no voltage across it and acts like a short circuit, which allows the maximum initial current to flow through the resistor. As the capacitor charges, the current decays exponentially, and the voltage across the capacitor increases until it eventually equals the source voltage. This transient behavior is key in analyzing the dynamics of charging in RC circuits.

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