Two identical resistors are connected in parallel to a 6 V battery, The total power dissipated in the circuit is 12 W. The current in each resistor is:

Correct option is D

Tha correct ans is (d)1.0A

• Battery Voltage (V) = 6 V
• Total Power dissipated in the circuit (P) = 12 W
• Two identical resistors are connected in parallel.

We need to find the current in each resistor.

The formula for power in a circuit is:$$P = I_{\text{total}}^2 R_{\text{eq}}P$$​​

Where:

• $P$ is the total power,
• ItotalI_{\text{total}}Itotal​ is the total current,
• ReqR_{\text{eq}}Req​ is the equivalent resistance of the parallel combination of the resistors.

We know that the total power dissipated is 12 W, and the voltage supplied is 6 V. So, using the formula for power:$$P = \frac{V^2}{R_{\text{eq}}}​$$​​

Substituting the given values:$$12 = \frac{6^2}{R_{\text{eq}}}\\ \ \\ ​ 12 = \frac{36}{R_{\text{eq}}}\\ \ \\R eq​ =3Ω$$​​

Now, using Ohm's law, the total current in the circuit is:$$Itotal = \frac{V}{R_{\text{eq}}}\\ \ \\I_{\text{total}} = \frac{6}{3} = 2 \, \text{A}I total​$$​​

Since the two resistors are identical and connected in parallel, the current divides equally between them. Therefore, the current through each resistor is:$$I_{\text{each}} = \frac{I_{\text{total}}}{2} = \frac{2}{2} = 1 \, \text{A}$$​​