The capacitor in an R C circuit (R=120 Ω, C=45 μF) is initially uncharged. Find (a) the charge o

step 1 The value of R in this problem is 120 and the value of C is equal to 45 micro ferret So the capa

The capacitor in an R C circuit (R=120 Ω, C=45 μF) is...

The capacitor in an $R C$ circuit $(R=120 \Omega, C=45 \mu \mathrm{F})$ is initially uncharged. Find (a) the charge on the capacitor and (b) the current in the circuit one time constant $(\tau=R C)$ after the circuit is connected to a $9.0-$ V battery.

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Key Concepts

RC Circuit

An RC circuit is a basic electrical circuit consisting of a resistor (R) and a capacitor (C) connected in series or parallel. It is used to study transient responses such as charging and discharging processes where the voltage or current changes exponentially over time.

Time Constant

The time constant, denoted by ? (tau), is defined as the product of the resistance and the capacitance (? = RC). It characterizes the rate at which the capacitor charges or discharges, indicating that after one time constant, a charging capacitor reaches approximately 63% of its final charge and the current decreases to about 37% of its initial value.

Capacitor Charging Behavior

The charging of a capacitor in an RC circuit follows an exponential behavior described by the equation Q(t) = C V (1 - e^(-t/RC)), where Q(t) is the charge at time t, C is the capacitance, V is the applied voltage, and RC is the time constant. Similarly, the current in the circuit decays exponentially as I(t) = (V/R) e^(-t/RC), reflecting the transient nature of the circuit immediately after a voltage is applied.

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