Question

If the resistance in the circuit is halved, what will be the current flowing through a 12-volt battery if there are initially 3.0 amps of current?

(1 point)
Responses

3.0 amps
3.0 amps

1.5 amps
1.5 amps

12 amps
12 amps

6.0 amps

Answer 1

To determine the new current when the resistance is halved, we can use Ohm's Law, which states that \( I = \frac{V}{R} \), where \( I \) is the current, \( V \) is the voltage, and \( R \) is the resistance.

1. Initially, the current is 3.0 amps. Let's denote the initial resistance as \( R_1 \) and the voltage as \( V = 12 \) volts.
2. Using Ohm's Law for the initial condition:
\[
I_1 = \frac{V}{R_1} \Rightarrow 3.0 = \frac{12}{R_1}
\]
Solving for \( R_1 \):
\[
R_1 = \frac{12}{3.0} = 4 \, \text{ohms}
\]

3. Now, if the resistance is halved, the new resistance \( R_2 \) will be:
\[
R_2 = \frac{R_1}{2} = \frac{4}{2} = 2 \, \text{ohms}
\]

4. Using Ohm's Law again to find the new current \( I_2 \):
\[
I_2 = \frac{V}{R_2} = \frac{12}{2} = 6 \, \text{amps}
\]

So the current flowing through the 12-volt battery when the resistance is halved will be **6.0 amps**.