Question 28: Current Electricity

Question

A galvanometer having a resistance of $50 \Omega$ is shunted by a wire of resistance $10 \Omega$. If the total current is 2 A , the current passing through the shunt is:

Accepted Answer

Understand the setup:
When a galvanometer is "shunted by a wire," it means the galvanometer and the shunt wire are connected in parallel. In a parallel circuit, the voltage across each branch is the same.
Identify the given values:
Resistance of the galvanometer ($R_g$) = $$50 \Omega$$
Resistance of the shunt wire ($R_s$) = $$10 \Omega$$
Total current ($I_{total}$) = $$2 	ext{ A}$$
Apply the voltage equality:
Let the current passing through the galvanometer be $I_g$ and the current passing through the shunt be $I_s$. Since the voltage across parallel components is the same, we have:
$$V_g = V_s$$
$$I_g R_g = I_s R_s$$
Apply Kirchhoff's Current Law:
The total current entering the parallel combination splits into the current through the galvanometer and the current through the shunt:
$$I_{total} = I_g + I_s$$
From this, we can express $I_g$ as:
$$I_g = I_{total} - I_s$$
Substitute and solve for $I_s$:
Now, let's substitute the expression for $I_g$ into our voltage equality equation:
$$(I_{total} - I_s) R_g = I_s R_s$$
Expand the equation:
$$I_{total} R_g - I_s R_g = I_s R_s$$
Move all terms with $I_s$ to one side:
$$I_{total} R_g = I_s R_s + I_s R_g$$
Factor out $I_s$:
$$I_{total} R_g = I_s (R_s + R_g)$$
Finally, solve for $I_s$:
$$I_s = \frac{I_{total} R_g}{R_s + R_g}$$
Plug in the numbers:
$$I_s = \frac{(2 	ext{ A}) 	imes (50 \Omega)}{10 \Omega + 50 \Omega}$$
$$I_s = \frac{100 	ext{ A}\Omega}{60 \Omega}$$
$$I_s = \frac{10}{6} 	ext{ A}$$
$$I_s = \frac{5}{3} 	ext{ A}$$
So, the current passing through the shunt is $$\frac{5}{3} 	ext{ A}$$.
Comparing this with the given options, it matches Option D.

Answer

$\frac{3}{5} \mathrm{~A}$

Answer

$\frac{2}{5} \mathrm{~A}$

Answer

$\frac{5}{6} \mathrm{~A}$

Answer

$\frac{5}{3} \mathrm{~A}$

Current Electricity

A galvanometer having a resistance of 50 \Omega is shunted by a wire of resistance 10 \Omega. If the total current is 2 A , the current passing through the shunt is:

Choose the correct answer: