Question

Derive the expression for the heat produced due to a current ‘I’ flowing for a time interval ‘t’ through a resistor ‘R’ having a potential difference ‘V’ across its ends. With which name is the relation known? How much heat will an instrument of 12W produce in one minute if it is connected to a battery of 12V?

Answer 1

Consider a resistor of resistance R. Let the current flowing through this resistor be I and the potential difference across it be V.

In time t, let Q amount of charge flows through the resistor.

Work done on moving this charge, W = VQ ... (1)

According to the definition of electric current,

`1=Q/t`

Q = I × t

Putting this in equation (1),

W = V × I × t

This work done is dissipated as heat.

Hence,

Heat produced, H = W = VIt

H = VIt ... (2)

According to Ohm’s law, V = IR.

Putting this in equation (2),

H = IR × It

H = I²Rt

This relation is known as Joule’s law of heating.

Power, P = 12 W

Potential difference, V =12 V

Time duration of current flow, t = 1 min = 60 s

`P = H/t`

H = P × t

= 12 W × 60 s

= 720 J

The heat generated by the instrument of 12 W in a minute is 720 J.