Question

The current through the circuit shown in figure is $1\, A$. If each of $4\, \Omega$ the resistors is replaced by $2\, \Omega$ resistor, the current in circuit will become nearly

• A. 1.11 A
• B. 1.25 A
• C. 1.34 A
• D. 1.67 A

Answer 1

Answer: (A)

In the circuit shown total external resistance $R=2\, \Omega+$ parallel combination of two $4\, \Omega$ resistors + parallel combination of three $15\, \Omega$ resistors.
$=2+\frac{4}{2}+\frac{15}{3}=2+2+5=9\, \Omega$
As $E=10\, V$ and $i=1\, A$, hence internal resistance $r$ of the cell should have a value given by
$E=i(R +r) $
$r=\frac{E}{i}-R=\frac{10}{1}-9=1\, \Omega$
If $4\, \Omega$ resistors are replaced by $2\, \Omega$ resistors, then as before $R'=2+\frac{2}{2}+\frac{15}{3}=2+1+5=8\, \Omega$
$\therefore $ New circuit current $i'=\frac{E}{R' +r}=\frac{10}{8+1}=1.11 \,A$