An ideal voltmeter is connected to the terminals of a real battery and is kept t

Question

An ideal voltmeter is connected to the terminals of a real battery and is kept there for the duration of the following experiments. (The voltmeter reads a positive value if its “+” terminal is at higher potential than its “–” terminal, and a negative value if the opposite is true.) Two separate measurements are made using the voltmeter, each with different connections in the hidden portion of the left branch.

In Experiment 1, there is an open connection in the hidden portion; that means there is a gap in the wire, so there is no physical connection on that branch. The voltmeter reads +V1.

In Experiment 2, there is a single resistor with resistance R0 in the hidden portion. The voltmeter reads +V2.

A. [2 pts] Determine the EMF of the battery in terms of some or all of the given variables (V1, V2, and/or R0). Show your work very neatly; convince the grader you understand the relevant physics.

B. [3 pts] Determine the internal resistance of the battery in terms of some or all of the given variables (V1, V2, and/or R0). Show your work very neatly; convince the grader you understand the relevant physics.

Explanation / Answer

a.

One can measure the e.m.f. of a battery by simply measuring the voltage across the terminals when it's not connected to anything. This is called measuring the voltage in 'open circuit'.

so, its value is V1

onecan't just measure the internal resistance directly because you can't get inside the battery. So you have to do an experiment where you change the current drawn from the battery (by changing the load resistance) and measuring the p.d. across the terminals.

Kirchoff's voltage law says that if you add up the voltages across all the components in a series circuit it must exactly equal the battery voltage.

e.m.f. = voltage across internal resistance + voltage across load (e.g. a bulb)

so, we can write : = Vinternal + VL

We know that V = IR, or using the appropriate terms for the internal resistance

Vinternal = Ir, so = Ir + VL

We can rearrange this equation to give VL = -rI +

If one set up a circuit with a variable resistor for the load then you can change the current, I, drawn from the battery and measure the voltage across the terminals, VL

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.