Circuit Components

RESISTOR:

Resistor is energy absorbing element in electrical circuit. It's unit is ohm.

The potential difference v across the terminals of resistor R, is directly proportional to the current i flowing through it.

That is,

           V=IR; Here R is called the resistance of resistor R

The reciprocal of resistance is defined as conductance( G).

Hence,

         (1/R)=G    &     I=VG

The power absorbed by a resistor is given by

         P=VI

INDUCTOR:

Inductor is an energy storing element in electrical circuit. It's unit is henry.

The potential difference v across the terminals of inductor is directly proportional to rate of change of current through it.

That is, $V = L\frac{{di}}{{dt}}$; Here the term L is the proportionality constant and known as inductance of the inductor.

Hence, current through inductor is

                                                     $I = \frac{1}{L}\int\limits_0^t {} Vdt + I(0)$

Where I(0) is the initial current of the inductor.

The energy stored in an inductor over the interval $\left( {{t_1},{t_2}} \right)$ is,

        $E\left( {{t_1},{t_2}} \right) = \int\limits_{{t_1}}^{{t_2}} {VIdt = \int\limits_{{t_1}}^{{t_2}} {L(dI/dt)} } Idt = \frac{L}{2}[\mathop I\nolimits^2 ({t_2})\_\mathop I\nolimits^2 ({t_1})]$

Inductor store the energy in the form of current.

CAPACITOR:

Capacitor is another energy storing element in electrical circuit. It's unit is farad.

The potential difference v between the terminals of capacitor is proportional to the charge q on it. That is

                                                                          $v \propto q$

                                                                           v=q/C; where C is the proportionality constant and is called the capacitance.

Now, $i = \frac{{dq}}{{dt}} = C(\frac{{dv}}{{dt}})$

         $\int {dv = \frac{1}{C}\int {idt} }$

Hence, $V(t) = \frac{1}{C}\int\limits_0^t {i(t)dt}  + q(0)/C$

where q(0) is the initial charge across the capacitor C.

The energy stored in a capacitor over the interval $\left( {{t_1},{t_2}} \right)$ is,

$E\left( {{t_1},{t_2}} \right) = \int\limits_{{t_1}}^{{t_2}} {VIdt = \int\limits_{{t_1}}^{{t_2}} {VC(dv/dt)} } dt = \frac{C}{2}[\mathop V\nolimits^2 ({t_2})\_\mathop V\nolimits^2 ({t_1})]$

Capacitor store the energy in the form of voltage.