Question

In the circuit shown in figure, after closing the switch $S$, what is the change in current flowing through the resistance $A$?

• A. No change in the value of current passing through resistance $A$
• B. The current passing through resistance $A$ decreases
• C. The current passing through resistance $A$ increases
• D. Data is insufficient to say anything

Answer 1

The correct option is A No change in the value of current passing through resistance $A$

Let us assign same electric potential to the points connected through same conducting wire in the given circuit.


Now redrawing the circuit, when switch $S$ is open.


Due to switch $S$ in open condition the resistance in that branch will vanish. Thus, there are effectively three resistances with value $r$ connected in parallel between points $1$ and $2$.

$\Rightarrow R_{\text{eq}}=\frac{r}{3}$

The current supplied by battery in the circuit will be,

$i_1=\frac{E}{\left(\frac{r}{3}\right)}=\frac{3E}{r}$

Since all the three resistances are identical, therefore current will get distributed equally in each of them.

Hence current through resistor $A$,

$i_A=\frac{i_1}{3}=\frac{E}{r}$

After the switch $S$ is closed:


We can observe that there are effectively four resistances with value $r$ connected in parallel between points $1$ and $2$.

$\Rightarrow R_{\text{eq}}=\frac{r}{4}$

The current supplied by battery in the circuit will be,

$i_2=\frac{E}{\left(\frac{r}{4}\right)}=\frac{4E}{r}$

Since all the four resistances are identical, therefore current will get distributed equally in each of them.

Hence current through resistor $A$,

$i_A=\frac{i_2}{4}=\frac{\left(\frac{4E}{r}\right)}{4}=\frac{E}{r}$

$\Rightarrow$The value of current through resistor $A$ will remain the same.

Why this question? $\underset{–}{\text{Tip}}:$In such problems always focus on obtaining a simple circuit by using point potential technique. The current will not flow in a branch in which the electrical path is broken, thus resistance in such paths can be neglected. $\underset{–}{\text{Caution}:}$In this question, the value of current through resistance $A$ has not changed due to identical resistance. However the current in circuit will increase after switch $S$ closed because $R_{\text{eq}}\downarrow$ for the circuit.