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Question

Two batteries with e.m.f. $$12$$V and $$13$$V are connected in parallel across a load resistor of $$10\Omega$$. The internal resistance of the two batteries are $$1\Omega$$ and $$2\Omega$$ respectively. The voltage across the load lies between.


A
11.4V and 11.5V
loader
B
11.7V and 11.8V
loader
C
11.6V and 11.7V
loader
D
11.5V and 11.6V
loader

Solution

The correct option is D $$11.5$$V and $$11.6$$V
Equivalent resistance of  $$r_1$$ and $$r_2$$,     $$r_{eq} = \dfrac{1\times 2}{1+2} = 0.66 \Omega$$
Equivalent emf of  $$E_1$$ and $$E_2$$,     $$E_{eq} = \bigg[\dfrac{E_1}{r_1}+\dfrac{E_2}{r_2}\bigg]r_{eq}$$
$$\implies \ $$ $$E_{eq} = \bigg[\dfrac{12}{1}+\dfrac{13}{2}\bigg]\times 0.66 = 12.33 \ V$$
Potential across  $$R$$,   $$V_R = \dfrac{R}{R+r_{eq}}E_{eq}$$
$$\implies \ $$  $$V_R = \dfrac{10}{10+0.66}\times 12.33 = 11.57 \ V$$
802275_845592_ans_c1d291d51d184e5485b0a180825fa88a.png

Physics

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