Six resistors, each of value 4 Ω, are joined together in a circuit as shown in the figure. Calculate equivalent resistance across the points A and B. If a cell of emf 2V is connected across AB, compute the current through the arms AB and DF of the circuit.

Solution

Given, 6 resistors of value 4Ω each joined together as shown in the circuit given.

The ratio of resistances on arms of the wheatstone bridge as shown in the equivalent circuit are equal.
Therefore, the balance condition of wheatstone bridge is satisfied.
Hence, no current flows (I_g = 0) in resistor R_g.
The circuit is agian redrawn as shown below.

R₁ and R₂ are in series combination.

∴ R_{12} = R_{1} + R_{2} = 4 + 4 = 8 Ω

and,

R_{34} = R_{3} + R_{4} = 8 Ω

Now, R_12,R₃₄ and R₅ are in parallel combination.
Therefore, equivalent resistance across AB is given by

\frac{1}{R} = \frac{1}{R_{12}} + \frac{1}{R_{34}} + \frac{1}{R_{5}}

\frac{1}{R} = \frac{1}{8} + \frac{1}{8} + \frac{1}{4} = \frac{4}{8} = \frac{1}{2}

R = 2 Ω

Current through arms

AB, I = \frac{V}{R} = \frac{2 V}{2 Ω} = 1 A

Current through arm DF = 0 ( represents the balanced condition of Wheatstone Bridge).

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Current Electricity

Six resistors, each of value 4 Ω, are joined together in a circuit as shown in the figure. Calculate equivalent resistance across the points A and B. If a cell of emf 2V is connected across AB, compute the current through the arms AB and DF of the circuit.

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