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Sunday, June 10, 2018

Three identical cells each have electromotive force (e.m.f.) E and negligible internal resistance



Question 5
Three identical cells each have electromotive force (e.m.f.) E and negligible internal resistance.
The cells are connected to three identical resistors, each of resistance R, as shown.

What is the potential difference between P and Q?
A 0                  B 3E                C 2E / 3                       D E





Reference: Past Exam Paper – November 2017 Paper 13 Q37





Solution:
Answer: C.

Two of the cells are providing an e.m.f. in one direction and the other in the opposite direction. So,
Overall e.m.f. = E + E – E = E

The resistors are connected in series.
Total resistance = R + R + R = 3R

From Ohm’s law, I = V / R
Current in circuit = overall e.m.f. / total resistance = E / 3R


Consider the potentials in the section PQ.

Let P be at a potential of E.
The e.m.f. of the cell is E. That is, the potential difference between the terminals of the cell is E. If point P is at a potential of 0, then the point between the positive terminal of the battery and the resistor is E.


Current in the circuit = E / 3R
p.d. V across a resistor = IR = (E/3R) × R = E / 3

Thus, potential at point Q = E – E/3 = 2E / 3


In another wording, potential difference between 2 points means the ‘difference in potential’ between the 2 points.
p.d. between P and Q = potential at Q – potential at P
p.d. between P and Q = 2E / R – 0 = 2E / R

2 comments:

  1. Why does P has a P.d of zero?

    ReplyDelete
    Replies
    1. it is taken arbitrarily. what is important is the the p.d. between the terminals of the cell is E.

      if the potential at P was E, then the potential at the other terminal would be 2E, such that the difference in potential is 2E - E = E.
      that is, the p.d. is still E.

      Delete

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