Question

what happens to the current in a circuit if a 10ω resistor is removed and replaced by a 20ω resistor?

Explanation:

Step1: Apply Ohm's Law

Ohm's Law is \(I = \frac{V}{R}\), where \(I\) is current, \(V\) is voltage, and \(R\) is resistance. Assume the voltage \(V\) of the circuit remains constant.

Step2: Analyze the change in resistance

Originally, with \(R_1=10\Omega\), \(I_1 = \frac{V}{10}\). After replacement, \(R_2 = 20\Omega\), \(I_2=\frac{V}{20}\).

Step3: Compare the currents

Since \(I_1=\frac{V}{10}\) and \(I_2=\frac{V}{20}\), and \(\frac{V}{20}=\frac{1}{2}\times\frac{V}{10}\), the current is halved.

Answer:

The current in the circuit is halved.