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

"\n

(A) Given:

Potential difference, $V=6V$

Resistance of the resistor, $R_1=1\Omega$

Resistance of the resistor, $R_2=2\Omega$

To find: Power used in $2\Omega$ resistor (when resistors are in series).

Solution:

We know that in a series combination, the current through each individual resistor is the same as the current through the circuit.

In series combination equivalent resistance is given as-

$R_{S}=R_1+R_2$

Putting the required values, we get-

$R_{S}=1+2$

$R_{S}=3\Omega$

Finding current in the circuit.

By Ohm's law, we have-

$V=I\times {R_S}$

Putting the required values, we get-

$6=I\times {3}$

$I=\frac {6}{3}$

$I=2A$

Now,

Finding power in $2\Omega$ resistor.

We know that electric power is given as-

$P=I^2\times R$

Putting the required values, we get-

$P=(2)^{2}\times 2$

$P=8W$

Thus, the power of the 2 Ohm resistor is 8 W.

(B) Given:

Potential difference, $V=4V$

Resistance of the resistor, $R_1=1\Omega$

Resistance of the resistor, $R_2=2\Omega$

To find: Power used in $2\Omega$ resistor (when resistors are in parallel).

Solution:

We know that in a parallel combination, the voltage through each resistor is the same as the total voltage in the circuit.

Hence, the potential difference or voltage across $2\Omega$ resistor is $4V$.

Now,

Finding power in $2\Omega$ resistor.

We know that electric power is given as-

$P=\frac {V^2}{R}$

Putting the required values, we get-

$P=\frac {(4)^{2}}{2}$

$P=\frac {16}{2}$

$P=8W$

Thus, the power of the 2 Ohm resistor is 8 W.

Comparing the power used in $2\Omega$ resistor in each of the following circuits, we can see that both have the same power.