A 12 V battery is set up in an unknown configuration. The internal resistance of the battery is 4 Ohms. If this circuit must have a minimum of two resistors, what resistance must these resistors have and what configuration must they be in in order for a terminal voltage to read 11.478 V? Show all work

Explanation:

Given that,

Battery capacity

E=12V

Internal resistance of battery r=4ohms

We are told that the circuit must have at least 2 resistor

If the terminal voltage is Vt= 11.478V

Let all the resistor we want to connect the battery have a equivalent resistance Req

Req = R1 +R2 + R3+...+ Rn

Series connection

Using KVL in the circuit,

E = I(R+r)

12 = I ( Req + 4) equation 1

When the terminal voltage is 11.478V, I.e voltage across the external resistance, in this case the equivalent resistance Req

Using ohms law

Vt=I•Req

Then,

11.478 = I•Req equation 2

Make I subject of formulae

Then, I = 11.478/Req. Equation 3

Substitute equation 3 into 1

12 = I ( Req + 4)

12 = 11.478/Req ( Rea + 4)

12 = 11.478 + 45.912/Req

12 - 11.478 = 45.912/Req

0.522 = 45.912/Req

Cross mutilply

0.522 Req = 45.912

Then, Req = 45.912/0.522

Req = 87.95 ohms

Req ≈ 88 ohms

The resistor must have a resistance of 88 ohms and they have a series configuration

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the amount of current in the coil