Question

Derive an expression for electric work connecting:

(a) Current, resistance, and time

(b) Current, potential difference, and time

(c)Potential difference, resistance, and time

Answer 1

Step 1:(b) Expression for electric work connecting current, potential difference, and time:

If '$W$‘ is the amount of work done in carrying a charge’$Q$ ‘from one point to another in an electric field such that potential is ’$V$' then

$W=VQ$ …….. (1)

But $Q=It$,where $I$ is current and $t$ is time.

Therefore equation (1) becomes,

$W=VIt$ … (2)

This is the expression for electric work in terms of current, potential difference, and time.

Step 2:(a)Expression for electric work connecting current, resistance, and time:

According to Ohm’s law,

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

Substitute, $V=IR$ in equation (2),

$W=VIt$

$W=IRIt$

$W=I^{2}Rt$ …….. (3)

This is the expression for electric work in terms of current, resistance, and time.

Step 4: (c )Expression for electric work connecting resistance, potential difference, and time:

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),

$W=VIt$

$W=V\frac{V}{R}t$

$W=\frac{V^{2}t}{R}$

This is the expression for electric work in terms of resistance, potential difference, and time.

Final Answer:

• The expression for electric work in terms of current, resistance, and time is $W=I^{2}Rt$
• The expression for electric work in terms of current, potential difference, and time is $W=VIt$
• The expression for electric work in terms of resistance, potential difference, and time is $W=\frac{V^{2}t}{R}$