Question

A Resistance coil of nichrome of resistance 50 ohm is joined to
a battery of 10 volt. The current is passed through it for 1 hour;
determine the produced heat in coil.​

Answer 1

7.2 KJ is the required answer.

GIVEN:

• Resistance, R = 50 ohm
• Potential difference, V = 10 volt
• Time, t = 1 hour

TO FIND:

Heat produced in the coil, H

FORMULAE:

• According to ohm's law, V = IR

• According to joule's law of heating, H = I²Rt

SOLUTION:

STEP 1: TO CONVERT TIME IN STANDARD UNITS

• SI unit of time is second.
• 1 hour = 60 minutes.
• 1 minute = 60 seconds.
• 60 minutes = 60 × 60 = 3600 seconds.
• 1 hour = 3600 seconds.

Time, t = 3600 seconds.

STEP 2: TO FIND CURRENT

$V = IR \\ \\ I = \frac{V}{R} \\ \\ I = \frac{10}{50} \\ \\ I = \frac{1}{5} \\ \\ I = 0.2 \: ampere$

Current through the coil is 0.2 A.

STEP 3: TO FIND HEAT

$H = {I}^{2} RT \\ \\ H = {(0.2)}^{2} \times 50 \times 3600 \\ \\ H = 0.2 \times 0.2 \times 50 \times 3600 \\ \\ H = 2 \times 2 \times 50 \times 36 \\ \\ H = 4 \times 50 \times 36 \\ \\ H = 200 \times 36 \\ \\ H = 7200 \: joules \\ \\ H = 7.2 \times {10}^{3} \: joules \\ \\ H = 7.2 \: kilo \: joules$

ANSWER:

Heat produced in the coil is 7.2 KJ

OTHER FORMULAE:

• H = VIt

• H = ( V²t) / R

JOULES LAW OF HEATING:

• According to the law, heat produced is directly proportional to the product of square of current, resistance and time.

• Heat is produced in the coil due to the resistance offered to the flow of current.