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Sunday, January 26, 2020

Two cells with electromotive forces E1 and E2 and internal resistances r1 and r2 are connected to a resistor R as shown.


Question 38
Two cells with electromotive forces E1 and E2 and internal resistances r1 and r2 are connected to a resistor R as shown.



The terminal potential difference across cell 1 is zero.

Which expression gives the resistance of resistor R?






Reference: Past Exam Paper – November 2019 Paper 12 Q34





Solution:
Answer: A.


Let the current in the circuit be I.

From Kirchhoff’s law,
Sum of e.m.f. in the circuit = Sum of p.d. in the circuit
E1 + E2 = I (r1 + r2 + R)
R + r1 + r2 = (E1 + E2) / I                     eqn (1)

However, none of the options available contains the current I. So, we need to substitute I by other quantities.


Consider the cell 1.
e.m.f. of cell 1 = terminal p.d. + lost volts

It is given that the terminal p.d. is zero. So,
e.m.f. of cell 1 = lost volts
E1 = I × r1
Current I = E1 / r1


Replace the current I in equation (1),
R + r1 + r2 = (E1 + E2) × r1 / E1
R + r1 + r2 = E1r1/E1 + E2r1/E1
R + r1 + r2 = r1 + E2r1/E1
R = r1 + E2r1/E1 – r1 – r2
R = E2r1/E1 – r2

Note that r2 can be written as E1r2/E1 so as to obtain the same denominator.
R = E2r1/E1 – E1r2/E1
R = (E2r1 –1r2) / E1

2 comments:

  1. thank you so much my brain almost exploded trying find out what is going on

    ReplyDelete
  2. Thanks I almost threw up tryin to solve

    ReplyDelete

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