Ncert Exercises & Solutions

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

Hint: Apply Ohm's law.

Step 1: Let the effective internal resistance of the batteries is

R_{eff}

. The effective external resistance R and the effective voltage of the batteries is

V_{eff}

Applying Ohm's law,

Then current through R is given by:

I = \frac{V_{eff}}{R_{eff} + R}

Step 2: If all the resistances and the effective voltages are increased n-times, then we have;

\begin{array}{l} V_{eff}^{new} = {nV}_{eff}, R_{eff}^{new} = {nR}_{eff} \\ R^{new} = nR \end{array}

Then, the new current is given by;

I' = \frac{{nV}_{eff}}{{nR}_{eff} + nR} = \frac{n (V_{eff})}{n (R_{eff} + R)} = \frac{(V_{eff})}{(R_{eft} + R)} = I

Thus, the current remains the same.

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