How Do You Calculate the Resistance of a Voltmeter?

[moenste]

Homework Statement

A battery is known to have an EMF of 5.0 V but when a certain voltmeter is connected to it the reading is 4.9 V. The battery can deliver a current of 0.40 A when connected to a resistance of 12 Ω. What is the resistance of the voltmeter?

Answer: 24.5 Ω.

2. The attempt at a solution
Let's find the internal resistance first: E = I (r + R) → 5 = 0.40 = (r + 12) → r = 0.5 Ω.

Then we have 4.9 = 5 - I r → I = 0.2 A and the resistance is R = V / I = 4.9 / 0.2 = 24.5 Ω.

Is this correct? I am mostly unsure why do we look for current in here 4.9 = 5 - I r. The internal resistance is in series with the battery and the current is equal to 0.4 A.

 

[gneill]

Is this correct? I am mostly unsure why do we look for current in here 4.9 = 5 - I r. The internal resistance is in series with the battery and the current is equal to 0.4 A.

The current is not 0.4 A when it's just the meter attached to the battery. The 0.40 A occurs when the 12 Ω resistor is connected to the battery. They are two separate experiments.

 

[moenste]

The current is not 0.4 A when it's just the meter attached to the battery. The 0.40 A occurs when the 12 Ω resistor is connected to the battery. They are two separate experiments.

View attachment 106878

Case 2 is the original case, right?

 

[gneill]

Case 2 is the original case, right?

What do you consider to be the original case?

 

[moenste]

What do you consider to be the original case?

E = 5 V, I = 0.4 A, R = 12 Ohm.

 

[gneill]

E = 5 V, I = 0.4 A, R = 12 Ohm.

Then yes, that's what's depicted in Case 2.

 

[David Lewis]

A simplifying assumption was made that battery source impedance is invariant with respect to current.