A 15.19-mF capacitor is fully charged using a battery that supplies Vemf =131.1 V. The battery

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A 15.19-mF capacitor is fully charged using a battery that...

A $15.19-\mathrm{mF}$ capacitor is fully charged using a battery that supplies $V_{\text {emf }}=131.1 \mathrm{~V}$. The battery is disconnected, and a $616.5-\Omega$ resistor is connected across the capacitor. What current will be flowing through the resistor after 3.871 s?

Key Concepts

RC Circuit

An RC circuit is a basic electrical circuit composed of a resistor and a capacitor. In the context of the given problem, it is relevant because the capacitor is discharging through a resistor, which leads to changes in voltage and current over time. Understanding how these components work together is key to analyzing the dynamic behavior of the circuit.

Time Constant

The time constant in an RC circuit, defined as the product of the resistance (R) and the capacitance (C), is crucial in determining the rate at which the capacitor discharges. It characterizes the speed of the exponential decay of the current and the voltage, indicating the time required for these values to drop to about 37% of their initial values.

Exponential Decay

Exponential decay describes how the current in an RC discharging circuit decreases over time according to the expression I(t) = I0 * exp(-t/RC). This concept is essential for predicting the current at any given moment, particularly after a specified duration, by using the initial current and the calculated time constant.

Ohm's Law in Transient Analysis

Ohm's Law, which relates voltage, current, and resistance, is important in transient analysis of RC circuits. It is used to determine the initial conditions such as the initial current (obtained by dividing the supply voltage by the resistance) when the capacitor begins to discharge, setting the stage for applying the exponential decay model.

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