Question:
Suppose there is a circuit consisting of only resistances and batteries and we have to double all voltages and all resistances. Show that currents are unaltered.
Solution:
Reff is the equivalent internal resistance of the battery
Veff is the equivalent voltage of the battery
Using Ohm’s law,
I = Veff/(Reff + R)
When the resistance and effective voltage are increased by n-times,
Veff = nVeff
Reff = n Reff
Rnew = nR
Then current is given as
I’ = bVeff/nReff + nR = Veff/Reff + R = I
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