Question

In a circuit, the equation for alternating voltage \( V \) is represented by \( V = 40 \sin(100 \pi t) \) volt. Here \( t \) is in seconds. Draw the time-voltage (t-V) graph with proper scale for one cycle. Calculate the root mean square value of voltage.

Hint:

For a sinusoidal voltage, the RMS value is the effective value that gives the same heating effect as a DC voltage of the same value.

Answer 1

- Time-Voltage graph: \includegraphics[]{t-v.PNG} The voltage equation is \( V = 40 \sin(100 \pi t) \). This represents a sinusoidal voltage, and the time period \( T \) is: \[ T = \frac{1}{f} = \frac{1}{50} = 0.02 \, \text{seconds}. \] The graph will have a peak voltage of 40 V, oscillating between +40 V and -40 V, completing one cycle every 0.02 seconds. - Root Mean Square (RMS) value: The RMS value of a sinusoidal voltage is given by: \[ V_{\text{rms}} = \frac{V_{\text{max}}}{\sqrt{2}}. \] Substituting \( V_{\text{max}} = 40 \): \[ V_{\text{rms}} = \frac{40}{\sqrt{2}} \approx 28.28 \, \text{V}. \]