Physics Q&A: Internal Resistance in Series with Variable Resistor

[Nabbsy88]

Hi, I am in yr 11 and i study physics I am my free time but have stumnbled across the following question that i can't seem to find an answer for in any books, would someone please be able to help me?

A cell is connected in series with a variable resistor. A high resistance voltmeter is connected across the terminals of the cell. When the variable resistor is set at 13Ohms the voltmeter reads 1.30V. And when the Variable resistor reads 8Ohms the voltmeter reads 1.20V. Find:

A) The emf of the cell
B) The internal resistance of the cell.

Any help at all would be greatly appreciated
Thanks.

 

[Doc Al]

Here's a hint: Treat the cell as being a perfect voltage source in series with a resistance equal to its internal resistance. Note that when you change the resistance in the variable resistance the current flowing throught the cell changes; the current creates a voltage drop within the cell due to the internal resistance.

 

[quicknote]

First of all, it's great that you are studying physics in your free time and have come across this question. It shows a strong interest and curiosity in the subject. Let's break down the question and see how we can find the answers.

A) The emf (electromotive force) of a cell is the amount of energy that the cell can provide to the circuit. In this case, we can use Ohm's Law (V=IR) to find the emf. We know that the voltmeter reads 1.30V when the variable resistor is set at 13Ohms. So, using Ohm's Law, we can calculate the current (I) in the circuit, which is 1.30V/13Ohms = 0.1A. Now, when the variable resistor is set at 8Ohms, the voltmeter reads 1.20V. Using the same formula, we get a current of 1.20V/8Ohms = 0.15A. We know that the emf is constant, so we can set these two equations equal to each other: 0.1A = 0.15A. This gives us an emf of 1.5V.

B) The internal resistance of a cell is the resistance within the cell itself. To find this, we can use the formula E = IR + Ir, where E is the emf, I is the current, R is the external resistance (in this case, the variable resistor), and r is the internal resistance. We already know the emf (1.5V) and the current (0.1A and 0.15A), so we can plug those values in and solve for r. This gives us an internal resistance of 0.5Ohms.

I hope this helps you understand how to approach and solve this type of problem. Keep up the good work in your physics studies!