Question

When a battery connected across a resistor of 16 ohm the voltage across the resistor is 12v .When the same battery is connected across a resistor of 10 ohm voltage across it is 11v.The internal resistance of the battery in ohms is?

Answer 1

Answer:

2.86Ω

Explanation:

Resistance = 16 Ω (Given)

Potential = 12 V  (Given)

Therefore, by ohm's law -

I = 12/16

I = 0.75 A

ε = I(R + r)

where r is the internal resistance of the battery and ε is the e.m.f. 

ε = 0.75(16 + r)  ----eq(1)

ε = I (10 + r)

ε = 11/10 (10 + r)  ------eq(2) 

From  equations (1) and (2), 

0.75(16 + r) = 1.1(10 + r)

= 12 + 0.75r = 11 + 1.1r

= 1.1r - 0.75r = 12 - 11

= 0.35r = 1

r = 1/0.35

r = 2.86 Ω

Hence, the Internal Resistance of the Battery is 2.86Ω.