Question

find the value of unknown resistor X in the following circuit if no current flows through the section AO. Also calculate the current drawn by a circuit from the battery of emf 6V and negligible internal resistance​

Answer 1

It is given in the question that no current flows through the section AO. It happens only in the condition of balanced wheatstone bridge.

• The wheatstone bridge is the simplest example of an arrangement, the variants of which are used for a large number of electric measurements. The important applications of wheatstone bridge are metre bridge, Carey-Foster's bridge and Post office box.

In the balanced Wheatstone bridge, the resistance in arm BD is ineffective.

For a balanced Wheatstone bridge,

❖ AB / OB = AC / OC

By substituting the given values;

➙ 2/3 = 4/X

➙ X = 4 × 3/2

➙ X = 2 × 3

➙ X = 6Ω

♦ In upper branch two resistances of 2Ω and 4Ω are connected in series. Hence their equivalent resistance will be 2 + 4 = 6Ω

♦ Similarly in lower branch two resistances of 3Ω and 6Ω are also connected in series. Their equivalent resistance will be 3 + 6 = 9Ω

Now two resistances of 6Ω and 9Ω come in parallel$.$

➙ 1/r = 1/6 + 1/9

➙ 1/r = (3 + 2) / 18

➙ 1/r = 5/18

➙ r = 3.6Ω

Finally, two resistances of 3.6Ω and 2.4Ω come in series. Hence net equivalent resistance of the circuit will be...

➠ R = 3.6 + 2.4

➠ R = 6Ω

♦ Net current flow in the circuit :

⭆ V = I × R

⭆ 6 = I × 6

⭆ I = 1 A