AC Voltage Applied To A Resistor - Practice Questions & MCQ

AC voltage applied to a resistor:

When a constant voltage source or battery is applied across a resistor current is developed in resister. This current has a unique direction and flows from the negative terminal of a battery to positive terminal. The magnitude of the current remains constant as well. If Direction of current through resistor changes periodically then current is called alternating current.

Voltage V(t) is applied across resistance R. V(t) is sinusoidal voltage with peak V_m and time period T.

$
T=\frac{1}{f}=\frac{2 \pi}{\omega}
$
Where $f$ is frequency and $\omega$ is angular frequency. This kind of circuit is a purely resistive circuit. According to Kirchhoff's law -

$
\begin{aligned}
v(t) & =R i(t) \\
i(t) & =\frac{v(t)}{R} \\
i(t) & =\frac{V_m \sin (\omega t)}{R} \\
i_m & =\frac{V_m}{R} \\
i(t) & =i_m \sin (\omega t)
\end{aligned}
$
Here voltage and current has same frequency and both are in same phase. Therefore phase difference between current and voltage is 0 .

The maximum value of voltage is achievd at $\mathrm{t}=\mathrm{T} / 4$.
Peak current, $i_0=\frac{V_0}{R}$.

Power factor: 

Ratio of resistance and impedance. The power factor also denoted by $\cos \phi$.
power factor $=\cos (\phi)=1$
Power:

$
P=V_{r m s} i_{r m s}=\frac{V_0 i_0}{2}
$
Time difference

$
\text { T.D. }=0
$