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.
Answer & explanation
Correct answer: option 4
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,
$I_R=I_{net}$
$(2-V)-\frac{V-1}{2}=\frac{3V}{4}$
$⇒4(2-V)-2(V-1)=3V$
$⇒8-4V-2V+2=3V$
$⇒10-6V=3V$
$⇒V=\frac{10}{9}V$
$∴I_R=\frac{3}{4}×\frac{10}{9}=\frac{5}{6}A$