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Suppose there is a circuit consisting of only resistances and batteries and we have to double (or increase it to n-times) all voltages and all resistances. Show that currents are unaltered.

 

Answers (1)

Original:

EMF = V_1

Resistance = R + R_{eff}

Current = \frac{V_1}{R+R_{eff}}

New:

EMF = nV_1

Resistance =n( R + R_{eff})

Current =\frac{n(V_1)}{n(R+R_{eff})}= \frac{V_1}{R+R_{eff}}

The current flow will not change throughout the system.

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