Question

calculate the power used in the 2 ohm resistor in each of the following circuits:

1) a 4 V battery in parallel with 12 ohm and 2ohm resistors.

2) a 6 V battery in series with 1 ohm and 2 ohm resistors.

Answer 1

(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

P= v²/R

P= 4*4/2

P= 16/2= 8W

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

Answer 2

Answer:

Explanation: ii) 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=8 W

(i) 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. only current varies so we hv to find individual current not total  

P= v²/R

P= 4*4/2

P= 16/2= 8 W

∴ the power used by 2 Ω resistor is 8 W