Question

The current in 1 Ω resistor in the following circuit is ______.

Options

• 1 A

• 0.5 A

• 1.1 A

• 0.8 A

Answer 1

The current in 1 Ω resistor in the following circuit is 1 A.

Explanation:

Condition for balanced Wheatstone-bridge,

`"P"/"Q" = "R"/"S"`

`=> 5/1 = 50/10`

`=> 5/1 = 5/1`

So, it is a balanced wheatstone-bridge and hence no current will flow through the arm G.

The circuit can be redrawn as given below,

As, we know that in a series branch, same current flows.

Hence, from the KVL loop rule,

V_PQ = l₁(5 + 1) = 6l₁   ...(i)

and V_RS = (50 + 10)(1.1 - l₁)   ...(ii)

Since, for the parallel branches, the voltage drop across them remains same,

So, V_PQ = V_RS 

`=> 6l_1 = 60(1.1 - l_1)`   ...(using Eqs. (i) and (ii))

⇒ l₁(60 + 6) = 66

⇒ l₁ = 1 A

Hence, current of 1 A passes through 1 Ω resistance.