Find R (in Ω) in the circuit shown so that the current through the central 4 Ω resistor is zero. The left, middle and right branches contain 2 Ω, 4 Ω and R respectively, with the 10 V, 6 V and 4 V batteries oriented as in the source diagram.
Physics · Mixed Chapter
JEE Mains

Question

Find R (in Ω) in the circuit shown so that the current through the central 4 Ω resistor is zero. The left, middle and right branches contain 2 Ω, 4 Ω and R respectively, with the 10 V, 6 V and 4 V batteries oriented as in the source diagram.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Explanation: Zero current through the 4 Ω branch implies zero drop across that resistor. With the 6 V source orientation shown, use Kirchhoff’s voltage law around the outer branches and the resulting node voltage condition; solving for the unknown branch gives R=1 Ω. The diagram is essential to the polarity convention.