Question

When a battery is connected across a resistor of 16 ohm the voltage across the resistor is 12 volt when the same battery is connected across a resistor of 10 ohm voltage across it is 11 volt the internal resistance of the battery is?

Answer 1

Given conditions ⇒
Resistance = 16 Ω
Potential = 12 V.
∴ I = 12/16 [By Ohm's law]
⇒ I = 0.75 A.

Now, Using the Formula, 
ε = I(R + r)
where r is the Internal Resistance of the Battery and ε is the e.m.f. of the battery. 

ε = 0.75(16 + r)  ----eq(i)

We know that the e.m.f. of the battery will never change if the resistance or the potential will change. 

∴ ε = I (10 + r)
ε = 11/10 (10 + r)  ------eq(ii) 

From  equations (i) and (ii), 
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 2.86 Ω.


Hope it helps.