A galvanometer having a resistance of 8 ohmsis shunted by a wire of resistance 2 ohms. If thetotal current is 1 amp, the part of it passingthrough the shunt will be [1998]a)0.25 ampb)0.8 ampc)0.2 ampd)0.5 ampCorrect answer is option 'B'. Can you explain this answer?

Question

A galvanometer having a resistance of 8 ohmsis shunted by a wire of resistance 2 ohms. If thetotal current is 1 amp, the part of it passingthrough the shunt will be     [1998]a)0.25 ampb)0.8 ampc)0.2 ampd)0.5 ampCorrect answer is option 'B'. Can you explain this answer?

Answer

Given:
Resistance of galvanometer (G) = 8 ohms
Resistance of shunt (S) = 2 ohms
Total current passing through the circuit (I) = 1 ampere

To find:
The part of the current passing through the shunt (Ish)

Formula:
The total current passing through the circuit (I) can be divided into two parts: the current passing through the galvanometer (Ig) and the current passing through the shunt (Ish).
According to the principle of parallel circuits, the voltage across each branch is the same. Therefore, we can use Ohm's law to find the current passing through each branch.

Calculation:
1. Calculate the equivalent resistance (Req) of the circuit.
Since the galvanometer and shunt are in parallel, we can use the formula for the equivalent resistance of parallel resistors.

1/Req = 1/G + 1/S
1/Req = 1/8 + 1/2
1/Req = 1/8 + 4/8
1/Req = 5/8
Req = 8/5 = 1.6 ohms

2. Use Ohm's law to find the current passing through the galvanometer (Ig).
V = I * Req
V = 1 * 1.6
V = 1.6 volts
Since the galvanometer and shunt are in parallel, they have the same voltage across them.

3. Calculate the current passing through the shunt (Ish).
Ish = V / S
Ish = 1.6 / 2
Ish = 0.8 amperes

Therefore, the part of the total current passing through the shunt is 0.8 amperes. Hence, option (b) is the correct answer.

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