Given : r1 = 1Ω
r2 = 2 Ω
E1 = 3v
E2 = 4v
Total equivalent internal resistance
\(\cfrac{1}{r_{eq}}\) = \(\cfrac{1}{r_1}\) + \(\cfrac{1}{r_2}\)
\(\cfrac{1}{r_{eq}}\) = \(\cfrac{1}{1}\) + \(\cfrac{1}{2}\)
\(\cfrac{1}{r_{eq}}\) = \(\cfrac{3}{2}\)
req = \(\cfrac{2}{3}\)Ω
Equivalent emf of cell in parallel connection
Eeq = \(\left[\cfrac{E_1}{r_1}+\cfrac{E_2}{r_2}\right]r_{eq}\)
Eeq = \(\left[\cfrac{3}{1}+\cfrac{4}{2}\right]\times \cfrac23\)
Eeq = \(\left[\cfrac{6+4}2\right]\times \cfrac23\)
Eeq = 5 x \(\cfrac{2}{3}\)
Eeq = 3.3 v
potential difference across 5 Ω resistor
E = \(\left[\cfrac{R}{R+r_{eq}}\right]\) Eeq
E = \(\left[\cfrac{5}{5+\cfrac23}\right]\) x 3.3
= \(\cfrac{15}{17}\) x 3.3
= 2.9 v