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Two resistors of $3 Ω$ and an unknown resistor are connected in series across a $12 V$ battery. If the voltage drop across the unknown resistor is $6 V$ , then the current in the unknown resistor is ____ $A$ .

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Detailed Solution

Two resistors of

3 Ω

and an unknown resistor are connected in series across a

12 V

battery. If the voltage drop across the unknown resistor is

6 V

, then the current in the unknown resistor is

1 A

.
Given:

V_{1} = V_{2}

Total potential diffeence

= 12 V

Same current flows through each resistor of series combination, the potential drop across both

3 Ω

resistor will be the same (

V_{1} = V_{2}

)
The total potential difference in series will be equal to,

V = V_{1} + V_{2} + V_{3}

12 = V_{1} + V_{1} + 6

6 = {2 V}_{1}

V_{1} = 3 V

The resistance across the

3 Ω

resistance is

3 V

.
The current in the resistor

3 Ω

is,

I = \frac{V}{R}

I = \frac{3}{3}

I = 1 A

The current in the

3 Ω

resistor is

1 A

, as all the resistors are connected in a series connection, and therefore, the current in the unknown resistor is

1 A

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