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Alternating Current Circuits
Alternating currents and voltages are sinusoidal and vary with time. Alternating currents produce different responses in resistors, capacitors, and inductors than direct currents do.
Alternating currents and voltages
This shows the plot of alternating voltage and alternating current as a function of time in a circuit that has only a resistor and a source of alternating current — an ac generator.
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  | Current and voltage from an ac source through a simple resistor. |
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Because the voltage and current reach their maximum values at the same time, they are in phase. Ohm's law and the previous expressions for power are valid for this circuit if the root mean square (rms) of the voltage and the rms of the current, sometimes called the effective value, are used. These relationships are
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Ohm's law is expressed thus: VR = IR, where VR is the rms voltage across the resistor and I is the rms in the circuit.
Resistor-capacitor circuits
A circuit with a resistor, a capacitor, and an ac generator is called an RC circuit. A capacitor is basically a set of conducting plates separated by an insulator; thus, a steady current cannot pass through the capacitor. A time-varying current can add or remove charges from the capacitor plates.  
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  | An RC circuit for charging a capacitor. |
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Initially, at time t = 0, the switch (S) is open, and there is no charge on the capacitor. When the switch is closed, a current will pass through the resistor and charge the capacitor. The current will cease when voltage drop across the capacitor equals the potential of the battery (V). Once the capacitor reaches the maximum charge, the current will decrease to zero. The current is at maximum immediately after the switch is closed and decreases exponentially with time. The capacitive time constant (?), the Greek letter tau) is the time for the charge to decay to 1/ e...