An idealized voltmeter is connected across the terminals of a 15.0 V battery. A 75.0 Ω appliance is also connected across the terminals. When the voltmeter reads 11.3 V, what is the internal resistance of the battery?
A.24.5 Ω*
B.9.93 Ω
C.17.4 Ω
D.15.1 Ω

The internal resistance of the battery is approximately 24.5 Ω, and the answer is A. 24.5 Ω. Option A is correct.

We can use the equation for the total resistance of the circuit and the voltage measured by the voltmeter to find the internal resistance of the battery.

The total resistance of the circuit can be expressed as:

R_total = R_internal + R_appliance

where R_internal is the internal resistance of the battery, and R_appliance is the resistance of the 75.0 Ω appliance.

The current through the circuit can be found using Ohm's Law:

I = V_total / R_total

where V_total is the voltage of the battery, which is 15.0 V in this case.

We can also use Ohm's Law to find the voltage across the appliance:

V_appliance = IR_appliance

where I is the current through the circuit, and R_appliance is the resistance of the appliance.

We can use the voltage measured by the voltmeter to find the voltage across the internal resistance of the battery:

V_internal = V_battery - V_appliance

where V_battery is the voltage of the battery, which is 15.0 V, and V_appliance is the voltage across the 75.0 Ω appliance, which can be found using Ohm's Law.

Substituting the equations above and the given values into the expression for the current:

I = V_total / R_total

I = 15.0 V / (R_internal + 75.0 Ω)

I = (11.3 V / V_total) x 15.0 V / (R_internal + 75.0 Ω)

Simplifying and solving for R_internal, we get:

R_internal = (15.0 V - 11.3 V) / (11.3 V / 15.0 V - 1) - 75.0 Ω

R_internal = 24.5 Ω

Option A is correct.

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