Question

Two resistors of resistances 10 ohm and 20 ohm are joined in parallel. A potential difference of 12 V is applied across the combination. Find the power consumed by each resistor.

Answer 1

GIVEN:

• Resistance, R1 = 10 ohm
• Resistance, R2 = 20 ohm
• Potential difference, V = 12 volt

TO FIND:

Power across each resistor.

FORMULA:

Power , P = V²/ R

SOLUTION:

STEP 1:

• Since the resistors are connected in parallel, the potential difference across each resistors are same.

• Potential difference across 10 ohm resistor is 12 volt.

• Potential difference across 20 ohm resistor is also 12 volt.

STEP 2:

Let P1 be the power consumed by 10 ohm resistor.

$P_1 = \frac{ {V}^{2} }{R_1} \\ \\ = \frac{ {(12)}^{2} }{10} \\ \\ = \frac{12 \times 12}{10} \\ \\ = \frac{144}{10} \\ \\ P_1 = 14.4 \: watt$

Power across 10 ohm resistor is 14.4 watt.

STEP 3:

Let P2 be the power consumed by 20 ohm resistor.

$P_2 = \frac{ {V}^{2} }{R_2} \\ \\ = \frac{ {(12)}^{2} }{20} \\ \\ = \frac{12 \times 12}{ 20} \\ \\ = \frac{144}{20} \\ \\ = \frac{72}{10} \\ \\ P_2 = 7.2 \: watt$

Power across 20 ohm resistor is 7.2 watt.

ANSWER:

• Power consumed by 10 ohm resistor is 14.4 watt.

• Power consumed by 20 ohm resistor is 7.2 watt.

OTHER FORMULAE OF POWER:

• P = VI
• P = I²R
• P = w / t
• P = f • v

Where,

• w is the work done
• t is the time
• f is the force
• v is the velocity