MHT CET · Physics · Current Electricity

The deflection in galvanometer falls to ${(\frac{1}{4})}^{t h}$ when it is shunted by $3 Ω$ . If additional shunt of $2 Ω$ is connected in parallel to earlier shunt, the deflection in galvanometer falls to

A $\frac{1}{2}$
B $\left(\frac{1}{3}\right)^{r d}$
C $\left(\frac{1}{4}\right)^{t h}$
D $\left(\frac{1}{8.5}\right)^{t h}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\left(\frac{1}{8.5}\right)^{t h}$

Step-by-step Solution

Detailed explanation

I - \frac{I}{4} = \frac{3 I}{4}

\frac{R I}{4} = \frac{3 I}{4} \times 3

R = 9 Ω

I = I_{1} + I_{2}

...(1)

9 I_{1} = \frac{6}{5} I_{2}

...(2)

\Rightarrow

\frac{15}{2} I_{1} = I_{2}

Using equation (1)

I = I_{1} + \frac{15}{2} I_{1} = \frac{17}{2} I_{1}

I_{1} = \frac{2 I}{17}

I_{1} =

\frac{I}{17 / 2} = \frac{I}{8.5}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The deflection in galvanometer falls to 14th when it is shunted by 3 Ω . If additional shunt of 2 Ω is connected in parallel to earlier shunt, the deflection in galvanometer falls to

Step-by-step Solution

The deflection in galvanometer falls to ${(\frac{1}{4})}^{t h}$ when it is shunted by $3 Ω$ . If additional shunt of $2 Ω$ is connected in parallel to earlier shunt, the deflection in galvanometer falls to