Electronics/AC Voltage and Current

Relationship between Voltage and Current

Resistor

In a resistor, the current is in phase with the voltage always. This means that the peaks and valleys of the two waveforms occur at the same times. Resistors can simply be defined as devices that perform the sole function of inhibiting the flow of current through an electrical circuit. Resistors are commercially available having various standard values, nevertheless variable resistors are also made called potentiometers, or pots for short. In theory electricity is a method used to harness myriad numbers including symbols to give the notion on how circuits function on a schematic drawing

Capacitor

The capacitor is different from the resistor in several ways. First, it consumes no real power. It does however, supply reactive power to the circuit. In a capacitor, as voltage is increasing the capacitor is charging. Thus a large initial current. As the voltage peaks the capacitor is saturated and the current falls to zero. Following the peak the circuit reverses and the charge leaves the capacitor. The next half of the cycle the circuit runs mirroring the first half.

The relationship between voltage and current in a capacitor is: $i(t)=C{d(v(t)) \over dt}$ . This is valid not only in AC but for any function v(t). As a direct consequence we can state that in the real world, the voltage across a capacitor is always a continuous function of the time.

If we apply the above formula to a AC voltage (i.e. $v(t)=V\cdot sin(\omega t+\Phi )$ ), we get for the current a 90° phase shift: $i(t)=V\cdot \omega \cdot cos(\omega t+\Phi )$ .

In an AC circuit, current leads voltage by a quarter phase or 90 degrees. Note that while in DC circuits after the initial charge or discharge no current can flow, in AC circuits a current flows all the time into and out of the capacitor, depending on the impedance in the circuit. This is similar to the resistance in DC circuits, except that the impedance has 2 parts; the resistance included in the circuit, and also the reactance of the capacitor, which depends not only on the size of the capacitor, but also on the frequency of the applied voltage. In a circuit that has DC applied plus a signal, a capacitor can be used to block the DC, while letting the signal continue.

Inductor

In inductors, current is the negative derivative of voltage, meaning that however the voltage changes the current tries to oppose that change. When the voltage is not changing there is no current and no magnetic field.

In an AC Circuit, voltage leads current by a quarter phase or 90 degrees.

Voltage Defined as the derivative of the flux linkage:

$V(t)={d(Ni(t)) \over dt}$ Resonance

A circuit containing resistors, capacitors, and inductors is said to be in resonance when the reactance of the inductor cancels that of the capacitor to leave the resulting total resistance of the circuit to be equal to the value of the component resistor. The resonance state is achieved by fine tuning the frequency of the circuit to a value where the resulting impedance of the capacitor cancels that of the inductor, resulting in a circuit that appears entirely resistive.