Suppose there is a circuit consister of only resistance and batteries , suppose one is to double (or increase it to in n-times )all voltage and all resistances , show that currents are unalatered

Explanation

To solve the problem of showing that doubling (or increasing to n-times) all voltages and resistances in a circuit consisting only of resistors and batteries does not alter the current, we can follow these steps:

### Step 1: Understand the Original Circuit
Consider a circuit with multiple batteries (EMFs) and resistors. The total current \( I \) flowing through the circuit can be expressed using Ohm's Law:
\[ I = \frac{E_{\text{total}}}{R_{\text{total}}} \]
where \( E_{\text{total}} \) is the sum of all EMFs in the circuit and \( R_{\text{total}} \) is the sum of all resistances.
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