Question

A $7 \,V$ battery with internal resistance $2 \,\Omega$. and a $3 \,V$ battery with internal resistance $1 \,\Omega$ are connected to a $10 \,\Omega$ resistor as shown in figure,

• A. $0.27\,A$
• B. $0.31\,A$
• C. $0.031\,A$
• D. $0.53\,A$

Answer 1

Answer: (C)

Using Kirchhoffs law in loop A $P_2 \,P_1 \,DA$
$\therefore 10I_{1}+2I-7=0$
$10I_{1}+2I=7$
Using Kirchhoff's law in loop $P_{2}P_{1}CBP_{2}$
$-3+1\left(I-I_{1}\right)-10\,I=0$

$I-11I_{1}=3$;
$I=3+11\,I_{1}\quad\ldots\left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$,
$10\,I_{1}+2\left(3+11\,I_{1}\right)=7$;
$10\,I_{1}+6+22\,I_{1}=7$
$\therefore 32\,I_{1}=1$;
$I_{1}=1/32=0.031\,A$