CBSE Class 12 · 2020 · Current ElectricityShort Answer

(a) Two cells of EMF

E_{1}, E_{2}

and internal resistances

r_{1}, r_{2}

are connected in parallel across an external resistance

R

(the cells supporting each other). Deduce the equivalent EMF and internal resistance.
(b) If the two cells are identical, each of EMF

E = 5 V

and internal resistance

r = 2 Ω

, calculate the voltage across

R = 10 Ω

Solution

(a) For parallel cells,

I_{1} = \frac{E _{1} - V}{r _{1}}

I_{2} = \frac{E _{2} - V}{r _{2}}

, and

I = I_{1} + I_{2}

. Writing

V = E_{e q} - I r_{e q}

and comparing gives

E_{e q} = \frac{E _{1} r _{2} + E _{2} r _{1}}{r _{1} + r _{2}}

and

r_{e q} = \frac{r _{1} r _{2}}{r _{1} + r _{2}}

. (b) Identical cells:

E_{e q} = 5 V

r_{e q} = \frac{2 \times 2}{4} = 1 Ω

. Then

I = \frac{E _{e q}}{R + r _{e q}} = \frac{5}{11} A

and

V_{R} = I R = \frac{5}{11} \times 10 = \frac{50}{11} \approx 4.55 V .

CBSE Class 12 Board · 2020 · Subjective