Question

In the above network, R = 2 Ω and E = 12 V. The equivalent resistance of the above network and current through each branch of the network is
(a) 4 Ω and 2.5 A respectively.
(b) 2 Ω and 3 A respectively.
(c) 2 Ω and 6 A respectively.
(d) None of the above.

Answer 1

We know for resistance

• In series =R= R₁+ R₂
• In parallel = 1/R = 1/R₁ +1/R₂

The given question is of a Wheatstone bridge.

We can omit the resistance connected in the center.

For calculating the equivalent resistance,

• Upperside has two resistance connected in series(R+R=2R) = 4Ω
• The lower side has two resistance connected in series(R+R=2R) = 4Ω
• Both the sides are connected parallelly.
• Hence, the equivalent resistance,( 1/R = 1/2R +1/2R=1/R) = 2Ω
• The equivalent resistance is 2Ω.

According to Ohms Law,

• V= IR
• V= 12V( Given)
• R =2Ω
• I = 6A in the complete circuit.

However, in each branch, the current would be equally distributed.

So, the upper branch and the lower branch have a current of 3 A.

The correct option is (b) 2 Ω and 3 A, respectively.