With a 1500 M resistor across its terminals, the terminal voltage of a certain b

Question

With a 1500 M resistor across its terminals, the terminal voltage of a certain battery is 2.60 V . With only a 5.11 resistor across its terminals, the terminal voltage is 1.80 V .

Part A

Find the internal emf of this battery.

Express your answer in volts to three significant figures.

part B

Find the internal resistance of this battery.

Express your answer in ohms to three significant figures.

Part C

What would be the terminal voltage if the 5.11 resistor were replaced by a 7.11 resistor?

Express your answer in volts to three significant figures.

Explanation / Answer

A) terminal voltage = E - Ir

where E = emf of battert, I = current in battery , r = internal resistor.

and I = E / (r + R)

V = E - (E/(r + R))r

V = (Er + ER - Er) / (r + R)

Vr + VR = ER

ER - Vr = VR

1500 x 10^6 E - 2.60r = 2.60 x 1500 x 10^6

1500 x 10^6 E - 2.60r = 3900 x 10^6 .......(i)

5.11E - 1.80r = 1.80 x 5.11

5.11E - 1.80r = 9.198 ......(ii)

solving,

E = 2.60 volt ........Ans(A)

r = 2.27 ohm /..........Ans(B)

C) now R = 7.11 ohm

ER - Vr = VR

2.60 x 7.11 - V(2.27) = V(7.11)

V = 1.97 volt ...........Ans

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