What happens to the current when both the voltage and resistance in a circuit are doubled?

When both the voltage and resistance in a circuit are doubled, the current can be analyzed using Ohm’s Law, which states that current (I) is equal to the voltage (V) divided by the resistance (R):

[ I = \frac{V}{R} ]

Let’s consider the initial conditions where the original voltage is ( V_0 ) and the original resistance is ( R_0 ). The current would then be:

[ I_0 = \frac{V_0}{R_0} ]

Now, if both the voltage and resistance are doubled, the new values will be ( 2V_0 ) for voltage and ( 2R_0 ) for resistance. Plugging these values into Ohm's Law gives:

[ I = \frac{2V_0}{2R_0} ]

When you simplify this equation, it becomes:

[ I = \frac{V_0}{R_0} ]

Thus, the current after both the voltage and resistance are doubled remains the same as the original current ( I_0 ). This demonstrates that when voltage and resistance increase in proportion, the current does not change because the ratio remains constant.