Question 197: Current Electricity

Question

The total length of potentiometer wire AB is 50 cm in the arrangement as shown in the figure. If
P
is the point where the galvanometer shows zero reading then the length AP is ________ cm.

Accepted Answer

When the galvanometer (G) shows a zero reading, it means no current is flowing through the galvanometer branch. This occurs when the circuit is in a balanced state.
Resistance $\mathrm{R}_1=6 \Omega$.
Resistance $\mathrm{R}_2=4 \Omega$.
Let the length be l . Its resistance is $\mathrm{R}_{\mathrm{AP}}$.
Since the total length AB is 50 cm , the length of PB is ( $50-\mathrm{l}$ ). Its resistance is $\mathrm{R}_{\mathrm{PB}}$.
The resistance R of a uniform wire is given by the formula :
$$ \mathrm{R}=\frac{\rho \mathrm{L}}{\mathrm{~A}} $$
Where $\rho$ is resistivity, L is length, and A is the cross-sectional area. Since the wire is uniform, the resistance is directly proportional to the length ( $\mathrm{R} \propto \mathrm{L}$ ).
$$ \mathrm{R}_{\mathrm{AP}}=\mathrm{k} \cdot \mathrm{l} $$
$$\Rightarrow $$ $$ \mathrm{R}_{\mathrm{PB}}=\mathrm{k} \cdot(50-\mathrm{l}) $$
where $\mathrm{k}=\frac{\rho}{\mathrm{A}}$ is a constant.
For a balanced bridge:
$$ \frac{\mathrm{R}_1}{\mathrm{R}_2}=\frac{\mathrm{R}_{\mathrm{AP}}}{\mathrm{R}_{\mathrm{PB}}} $$
Substituting the known values :
$$ \frac{6}{4}=\frac{\mathrm{k} \cdot \mathrm{l}}{\mathrm{k} \cdot(50-\mathrm{l})} $$
$$\Rightarrow $$ $\frac{3}{2}=\frac{1}{50-1}$
$$\Rightarrow $$ $3(50-l)=2 l$
$$\Rightarrow $$ $150-3 l=2 l$
$$\Rightarrow $$ $150=5l$
$$\Rightarrow $$ $$ \mathrm{l}=\frac{150}{5}=30 \mathrm{~cm} $$
Therefore, the length of AP is 30 cm . Hence, the correct option is (B).

Answer

25

Answer

30

Answer

15

Answer

20

Current Electricity

The total length of potentiometer wire AB is 50 cm in the arrangement as shown in the figure. If P is the point where the galvanometer shows zero reading then the length AP is ________ cm.

Choose the correct answer: