The current through a $4 / 3 \Omega$ external resistance connected to a parallel combination of two cells of 2 V and 1 V emf and internal resistances of $1 \Omega$ and $2 \Omega$ respectively is _______.

Fill in the blank with the correct answer from the options given below.

5/6 A

The correct answer is Option (4) → 5/6 A

EMF, $E_1=2V$ with internal resistance, $r_1=1Ω$

EMF, $E_21=1V$ with internal resistance, $r_2=2Ω$

let the common node voltage be V.

from cell 1:

Current, $I_1=\frac{E_1-V}{r_1}=\frac{2-V}{1}=2-V$

$I_2=\frac{V-E_2}{r_2}=\frac{V-1}{2}$

and,

$I_{net}=I_1-I_2=(2-V)-\frac{V_1}{2}$

Load current, $I_R=\frac{V}{R}=\frac{V}{\frac{4}{3}}=\frac{3V}{4}$

By Kirchoff's junction law,

$I_R=I_{net}$

$(2-V)-\frac{V-1}{2}=\frac{3V}{4}$

$⇒4(2-V)-2(V-1)=3V$

$⇒8-4V-2V+2=3V$

$⇒10-6V=3V$

$⇒V=\frac{10}{9}V$

$∴I_R=\frac{3}{4}×\frac{10}{9}=\frac{5}{6}A$