A capacitor is fully charged using a battery that supplies Ve mf=133.1 V The battery is disconn

step 1 As we all know that the value of IT is equal to VEMF by R multiplication E to the power minus T

A capacitor is fully charged using a battery that supplies...

A capacitor is fully charged using a battery that supplies $V_{e \mathrm{mf}}=133.1 \mathrm{~V}$ The battery is disconnected, and a $655.1-\Omega$ resistor is connected across the capacitor. The current flowing through the resistor after $1.743 \mathrm{~s}$ is $0.1745 \mathrm{~A}$. What is the capacitance of the capacitor?

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Key Concepts

RC Circuit

An RC circuit consists of a resistor and a capacitor connected in series or parallel. In such circuits, the capacitor charges or discharges through the resistor, and the behavior is governed by a first?order differential equation that shows how voltage and current change over time.

Time Constant

The time constant, represented by ? (tau), is the product of the resistance (R) and the capacitance (C) in an RC circuit. It indicates the rate at which the capacitor charges or discharges; after one time constant, the voltage or current changes by about 63.2% of the difference between its initial value and its final value.

Exponential Decay

Exponential decay describes the way variables like voltage and current decrease over time in RC circuits. This decay is expressed mathematically by an exponential function, reflecting the rapid initial change that slows as time progresses, and is crucial in determining circuit behavior during transient analysis.

Capacitor Discharge Equation

In the context of a discharging capacitor, the current through a resistor follows the relationship I(t) = (V0/R) exp(-t/RC), where V0 is the initial voltage across the capacitor. This equation is fundamental for analyzing how the current decreases over time and for calculating unknown parameters such as the capacitance.

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