The plot of the variation of potential difference across a combination

1.	The plot of the variation of potential difference across a combination of three identical cells in series, versus current is shown alongside. What is the emf and internal resistance of each cell?
Answer» We know that for a circuit V = E_eq - Ir_eq ....(i) From graph, when I = 0 A, then V = 6 V and when I = 1 A then V = 0 V Putting V = 6 V and I = 0 A in eq (i) 6 = E_eq - 0.r_eq \(\Rightarrow\) E_eq= 6 V E_eq = ε₁+ ε₂ + _ε3\(\Rightarrow\) ε₁= ε₂ = ε₃ = ε = \(\frac{E}{3}\) = 2 V And, when I = 1 A, and V = 0 V 0 = 6 - 1. r_eq \(\Rightarrow\) r_eq = 6 Ω r_eq= r₁+ r₂ + r₃ \(\Rightarrow\) r₁= r₂ = r₃= r = \(\frac{R}{3}\) = 2 ohm

The plot of the variation of potential difference across a combination of three identical cells in series, versus current is shown alongside. What is the emf and internal resistance of each cell?

Answer»

We know that for a circuit

V = E_eq - Ir_eq ....(i)

From graph, when I = 0 A, then V = 6 V and when I = 1 A then V = 0 V

Putting V = 6 V and I = 0 A in eq (i)

6 = E_eq - 0.r_eq \(\Rightarrow\) E_eq= 6 V

E_eq = ε₁+ ε₂ + _ε3\(\Rightarrow\) ε₁= ε₂ = ε₃ = ε = \(\frac{E}{3}\) = 2 V

And, when I = 1 A, and V = 0 V

0 = 6 - 1. r_eq \(\Rightarrow\) r_eq = 6 Ω

r_eq= r₁+ r₂ + r₃ \(\Rightarrow\) r₁= r₂ = r₃= r = \(\frac{R}{3}\) = 2 ohm