An uncharged capacitor and a resistor are connected in...

An uncharged capacitor and a resistor are connected in series to a source of emf. If $\varepsilon=9.00 \mathrm{~V}, C=20.0 \mu \mathrm{F}$, and $R=100 \Omega$, find (a) the time constant of the circuit, (b) the maximum charge on the capacitor, and (c) the charge on the capacitor after one time constant.

An uncharged capacitor and a resistor are connected in series to a source of emf. If $\varepsilon=9.00 \mathrm{~V}, C=20.0 \mu \mathrm{F}$, and $R=100 \Omega$, find (a) the time constant of the circuit,
(b) the maximum charge on the capacitor, and (c) the charge on the capacitor after one time constant.

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Key Concepts

Maximum Capacitor Charge

The maximum charge that a capacitor can hold in a DC circuit is given by the product of its capacitance and the electromotive force of the source (Qmax = C × V). This represents the steady-state charge when the capacitor is fully charged and no further current flows.

RC Time Constant

The time constant in an RC circuit is defined as the product of the resistance and the capacitance (? = R × C). It characterizes the rate at which the capacitor charges or discharges, determining how quickly the capacitor reaches about 63% of its final value during charging, or decays to about 37% during discharging.

Exponential Charging Equation

The charging of a capacitor in an RC circuit follows an exponential behavior expressed by Q(t) = Qmax (1 - e^(-t/RC)). This formula describes how the capacitor gradually accumulates charge over time, approaching its maximum charge asymptotically as time increases.

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