Question

Derive an expression for electric power connecting:

(a) Current and resistance

(b) Current and potential difference

(c)Potential difference and resistance

Answer 1

Step 1:Expression for electric power:

$P=\frac{W}{t}$ …….(1) ,

Here $P$ is power, $W$ is electric work done and $t$ is time.

Step 2:(a) Expression for electric power connecting current and resistance:

We know the work done formula in terms of current ,resistance and time ,as

$W=I^{2}Rt$

Substitute $W=I^{2}Rt$ in equation (1)

$$\begin{gathered} P=\frac{I^{2}Rt}{t} \\ P=I^{2}R \end{gathered}$$

This is the expression for electric power in terms of current and resistance.

Step 3:(b)Expression for electric power connecting current and potential difference:

We know the work done formula in terms of current $\text{'}I\text{'}$,potential difference$\text{'}V\text{'}$ and time$\text{'}t\text{'}$ ,as

$W=VIt$

Substitute $W=VIt$ in equation (1)

$P=\frac{VIt}{t}$

$P=VI$ ……..(2)

This is the expression for electric power in terms of current and potential difference.

Step 4:(c )Expression for electric power connecting resistance and potential difference:

From Ohm’s law,

$V=IR$, where $V$ is potential difference or voltage and $R$ is resistance.

We can rewrite $V=IR$ as,

$I=\frac{V}{R}$

Substitute $I=\frac{V}{R}$ in equation (2),

$$\begin{gathered} P=V\frac{V}{R} \\ P=\frac{V^2}{R} \end{gathered}$$

This is the expression for electric power in terms of resistance and potential difference.

Final Answer:

1. The expression for electric power in terms of current and resistance is $P=I^{2}R$
2. The expression for electric power in terms of current and potential difference is $P=VI$
3. The expression for electric power in terms of resistance and potential difference is $P=\frac{V^2}{R}$