2021 Solution 03
2021 Solution 03
Isaac P Abraham
2020 Dec 25
2020 Dec 25
Two batteries are connected in series as shown. Each battery exhibits a potential E with an internal resistance R. What is the voltage measured by a voltmeter across nets A, B?
● Rather than work with floating voltages V(A) and V(B) let us designate net B as an arbitrary reference where V(B)=0 (or any potential P).
● Let the current in the circuit be I, circulating clockwise. For the top branch,
● Let the current in the circuit be I, circulating clockwise. For the top branch,
V(A)+E-I*R=P
(
1
)For the lower branch,
P+E-I*R=V(A)
(
2
)Subtract (2) from (1)
V(A)+E-I*R-P-E+I*R=P-V(A)
(
3
)2*V(A)=2P
(
4
)V(A)=P
(
5
)Both nets are at the same potential P.
The voltmeter measures the difference in voltage V(A)-V(B) = 0 V.
Ref: Valerii Ilyushchenko (translated by V.N. Lange), "Science for everyone", Mir Publishers, Moscow, USSR.