Two cells of emf E 1 and E 2 have internal resistance r 1 and r 2 . Deduce an expression for equivalent emf of their parallel combination.

Question

Philoid · Accepted Answer

We have two cells E₁ and E₂ with internal resistance r₁ and r₂ connected in parallel with a resistor R.
Let, I₁ and I₂ be the current through E₁ and E₂ respectively.
By applying KCL(Kirchhoff's Current Law),

I = I₁ + I₂
Let their resultant EMF is E_eff

resultant resistance be R_eq.
By KVL(Kirchhoff's Voltage Law)

Potential across
Potential across upper branch =
Potential across Lower Branch =
After solving we will get
and

Two cells of emf E1 and E2 have internal resistance r1 and r2. Deduce an expression for equivalent emf of their parallel combination.

Two cells of emf E₁ and E₂ have internal resistance r₁ and r₂. Deduce an expression for equivalent emf of their parallel combination.