Root Mean Square Voltage/Current

The Effective Voltage for a Sinusoidal Alternating Current

1. The maximum potential difference supplied by an a.c source is known as the peak voltage V_P. 
2. The effective potential difference for an a.c is equal to the potential difference of a alternating current if both results in the same heating effect. 
3. The effective potential difference for a.c is known as the root mean square voltage (r.m.s) of the a.c. and is given y the following equation:

$$V_{rms}=\frac{V_p}{\sqrt{2}}$$

4. The root-mean-square (r.m.s) value of an alternating current is the value of the steady direct current which produces the same power in a resistor as the mean power produced by the alternating current. 
5. The r.m.s current is the effective value of the alternating current.
6. The r.m.s. current can be calculated by using the following equation:

$$I_{rms}=\frac{I_p}{\sqrt{2}}$$

Example 1

Diagram above shows a graph of potential difference, V against time, t of an alternating current. Find the V_r.m.s. of the power supply.

Answer:
$$\begin{array}{l}{V}_{rms}=\frac{V_p}{\sqrt{2}}\\ V_{rms}=\frac{(14)}{\sqrt{2}}=9.90V\end{array}$$

Example 2

The diagram above shows the wave form of an a.c. supply. What is the root mean square value of the current?

Answer:
$$\begin{array}{l}{I}_{rms}=\frac{I_p}{\sqrt{2}}\\ I_{rms}=\frac{(2)}{\sqrt{2}}=1.41\end{array}$$