# Circuit Elements

DC may be controlled only by resistor. But alternating current in a circuit may be controlled by three elements; resistor, inductor and capacitor. These elements are called circuit elements of AC. An AC circuit may contain some or all of them.

The properties of resistor, inductor and capacitor are referred as resistance, inductance and capacitance respectively. One element may also have all the three properties existing in it. For example, a coil has always some resistance and inductance, and also some interturn capacitance.

## Resistance

Resistance of a material of a conductor is its property which opposes the flow of charge. According to Ohm’s law, in dc circuit, the ratio of potential difference $(V)$ between two points and current $(I)$ through these two points is called resistance $(R)$. $R=\frac{V}{I}$ It is measured in ohm.

In ac circuit, the ratio $\frac{V}{I}$ is also called resistance. In the resistor, the current through the circuit is in same phase with the voltage across it. Resistance does not depend upon the frequency of ac. [AC Through a Resistor (AC Through Circuit Elements)]

## Reactance

The effective hindrance or opposition offered by inductor or capacitor or both to the flow of ac is called reactance. It is denoted by $X$.

### Inductive Reactance $(X_L)$

The reactance offered by an inductor alone is called inductive reactance. It is denoted by $X_L$. In the inductor, current lags behind voltage by phase $\frac{π}{2}$. In an AC circuit, $X_L=\omega L=2πfL$ where, $f$ is the frequency of ac and $L$ is the inductance of the inductor. [AC Through an Inductor (AC Through Circuit Elements)]

In DC circuits, $f=0$. $\therefore X_L=0$ Hence, a pure inductor offers zero resistance to dc.

Also, $X_L∝f$. Hence, higher the frequency of ac, more is the inductive reactance. Inductive reactance is measured in ohm.

### Capacitive Reactance $(X_C)$

The reactance offered by a capacitor alone is called capacitive reactance. It is denoted by $X_C$. In the capacitor, current leads voltage by a phase of $\frac{π}{2}$. In an AC circuit, $X_C=\frac{1}{\omega C}=\frac{1}{2πfC}$ where, $C$ is the capacitance of the capacitor. [AC Through a Capacitor (AC Through Circuit Elements)]

In DC circuits, $f=0$. $\therefore X_C=\infty$ Hence, a capacitor blocks DC current.

Also, $X_C∝\frac{1}{f}$. Hence, higher the frequency of ac, lower the capacitive reactance. Capacitive reactance is measured in ohm.

## Impedance

The total effective opposition offered by any two or all the three circuit elements to ac is called impedance of the circuit. It is denoted by $Z$. In general, impedance $Z$ comprises of all three parts; resistance $R$, inductive reactance $X_L$ and capacitive reactance $X_C$ where $X_L$ and $X_C$ are opposite to each other. Impedance is measured in ohm.

The term impedance is a general word which is used for any electrical opposition. Hence, resistance as well as reactance are the impedance.

The reciprocal of impedance of a circuit is called admittance of the circuit. It is denoted by $Y$. $\therefore Y=\frac{1}{Z}$ Its unit is ohm-1 or mho or siemen. It gives the information about to what extent the given ac circuit allows the current.

## Susceptance

The reciprocal of reactance of a circuit is called susceptance of the circuit. It is denoted by $S$. $\therefore S=\frac{1}{X}$ For inductor, $S_L=\frac{1}{X_L}$ For capacitor, $S_C=\frac{1}{X_C}$ Its unit is ohm-1 or mho or siemen. It measures how susceptible an element is to allow the current.

## Conductance

The reciprocal of resistance of a circuit is called conductance of the circuit. It is denoted by $G$. $\therefore G=\frac{1}{R}$ Its unit is ohm-1 or mho or siemen. Conductance is used for dc circuits. It gives the information about to what extent the resistor allows the dc.

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