10 cells, each of emf ‘E’ and internal resistance ‘r’, are connected in series to a variable external resistance. Fig. shows the variation of terminal potential difference of their combination with the current drawn from the combination. Emf each cell is:
Answers
Given,
10 cells, each of emf ‘E’ and internal resistance ‘r’, are connected in series to a variable external resistance R.
To find,
The Electromotive force (emf) of each cell.
see figure,
equation of line is ..
V/42 + i/14 = 1 ......(1)
as 10 cells each of end E and internal resistance r are connected in series to a variable resistance R.
then, terminal voltage, V = 10ER/(10r + R) putting it in equation (1) we get,
10ER/42(10r + R) + i/14 = 1
⇒10ER/(10r + R) + 3i = 42
⇒10ER + 3i(10r + R) = 42(10r + R)
⇒10E + 3i(10r/R + 1) = 42(10r/R + 1)
as R is variable, let's take R tends to infinity.
then, 10E + 3i = 42
E = (42 - 3i)/10
as R tends to infinity, i equals to zero.
so, E = 42/10 = 4.2 Volts.
Therefore emf of each cell is 4.2 volts.
