Question

With a 1500 MΩ resistor across its terminals, the terminal voltage of a certain battery is 2.63 V . With only a 5.10 Ω resistor across its terminals, the terminal voltage is 1.72 V .

Part A) Find the internal emf of this battery.

Part B) Find the internal resistance of this battery.

Part C) What would be the terminal voltage if the 5.10 Ω resistor were replaced by a 7.10 Ω resistor?

Answer 1

a)

When 1500 MΩ resistor is connected :

current in the circuit : I = 2.63/(1500*10^6) = 1.75*10^-9 A

So, Emf of battery, E = 1.75*10^-9*(1500*10^6 + r) <-------- r = internal resistance of the battery

Now, when 5.1 Ω resistor is connected :

E = (1.72/5.1)*(5.1 + r)

So, E = 1.75*10^-9*(1500*10^6 + r) = (1.72/5.1)*(5.1 + r)

So, r = 2.68 Ω <--------- answer (B)

So, E = 1.75*10^-9*(1500*10^6 + 2.68) = 2.63 V <-------- answer( A)

C)

Current in the circuit = 2.63/(7.1 + 2.68) = 0.269 A

So, terminal voltage = 0.269*7.1 = 1.91 V <----------- answer