Two cells, each of emf , having internal resistances and respectively, are connected…

PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity

Problem

Two cells, each of emf

E

, having internal resistances

r_{1}

and

r_{2}

respectively, are connected in series to an external resistor

R

. (i) Obtain an expression for the current

I

flowing in the circuit. (ii) Derive an expression for the terminal potential difference

V_{\text{series}}

of the combination under load. (iii) Show that when the circuit is open, the terminal potential difference equals

2E

, and that when current flows it decreases by

I(r_{1}+r_{2})

. Explain the physical significance of this decrease with reference to energy dissipation inside the cells. (iv) For a given value of

R

, determine the condition on

r_{1}

and

r_{2}

under which the power lost in the internal resistances equals the power delivered to the external resistor.