Compare the power used in the 2 Ω resistor in each of the following circuits

Question 14:

Compare the power used in the 2 Ω resistor in each of the following circuits: (i) a 6 V battery in series with 1 Ω and 2 Ω resistors, and (ii) a 4 V battery in parallel with 12 Ω and 2 Ω resistors.

Answer:

 (i) Potential difference (V) = 6 V

 Here 1 Ω and 2 Ω resistors are connected in series.

 ∴ equivalent resistance of the circuit (R) = 1 + 2 = 3 Ω

According to Ohm’s law

V = IR

Or I=V/R=6/3=2A

the current through the circuit (I)=2A

Now the power used in the 2 Ω resistor

we know that Power = I²R

                                 = 2×2×2=8W

(ii) Potential difference, V = 4 V

12 Ω and 2 Ω resistors are connected in parallel. The voltage across each component of a parallel circuit remains the same. Hence, the voltage across 2 Ω resistor will be 4 V. Power consumed by 2 Ω resistor is given by

∴ the power used by 2 Ω resistor is 8 W.