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
thank you so much my brain almost exploded trying find out what is going on
ReplyDeleteThanks I almost threw up tryin to solve
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