What is the current drawn from the cell in the circuit shown below. The galvanometer (G) resistance is 10Ω.

What is the current drawn from the cell in the circuit shown below. The galvanometer (G) resistance is 10Ω. What is the current drawn from the cell in the circuit shown below. The galvanometer (G) resistance is 10Ω

Right Answer is:

0.9 mA

SOLUTION

Balanced Wheatstone Bridge:

  • In a balanced Wheatstone bridge, the ratio of resistances in the two arms is equal. This means:

P/Q = R/S

In this specific case, the values are:

10/30 = 20/60

  • When the bridge is balanced, no current flows through the galvanometer. This is because the potential difference across the galvanometer is zero.
  1. Current Drawn from the Cell:
  • To find the current drawn from the cell, we need to calculate the equivalent resistance of the circuit.
  • 30 and 10 ohm resistance is connected in series and 20 ohm and 60 ohm are connected are connected in series.
  • The 40 kΩ and 80 kΩ resistors are connected in parallel. The equivalent resistance (Req) of two resistors in parallel is given by:

1/Req = 1/R1 + 1/R2

  • So, for the given resistors:

1/Req = 1/40kΩ + 1/80kΩ

Req = 80/3 kΩ

  • Now, we can use Ohm’s law to find the current (I) drawn from the cell:

I = V/Req

Where:

  • V = Voltage of the cell (24 V)
  • Req = Equivalent resistance (80/3 kΩ)
  • Substituting the values:

I = 24 V / (80/3 )

I = 0.9 mA

Therefore, the current drawn from the cell is 0.9 mA.

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