# 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. Do this for circuit of Example 3.7 in the NCERT Text Book for Class XII.

Original:

$EMF = V_1$

$Resistance = R + R_{eff}$

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

New:

$EMF = nV_1$

$Resistance =n( R + R_{eff})$

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

Increasing the EMF and Resistance in the same ratio (say 2), will not change the current flowing through the system.

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