Question
You have a series circuit with a current of 6 amps and three resistors on it, with resistances of 10 ohms, 5 ohms, and 6 ohms, respectively. What is the voltage of this circuit? Show your calculation.
Answers
GPT-4o mini
To find the voltage in a series circuit, you can use Ohm's Law, which states:
\[
V = I \times R
\]
where \( V \) is the voltage, \( I \) is the current, and \( R \) is the total resistance in the circuit.
1. First, calculate the total resistance \( R \) in the circuit. In a series circuit, the total resistance is simply the sum of all individual resistances:
\[
R_{\text{total}} = R_1 + R_2 + R_3
\]
Given:
- \( R_1 = 10 \, \text{ohms} \)
- \( R_2 = 5 \, \text{ohms} \)
- \( R_3 = 6 \, \text{ohms} \)
Calculating the total resistance:
\[
R_{\text{total}} = 10 \, \text{ohms} + 5 \, \text{ohms} + 6 \, \text{ohms} = 21 \, \text{ohms}
\]
2. Now, use the total resistance and the given current to find the voltage:
Given:
- \( I = 6 \, \text{amps} \)
Calculate the voltage:
\[
V = I \times R_{\text{total}} = 6 \, \text{amps} \times 21 \, \text{ohms} = 126 \, \text{volts}
\]
Therefore, the voltage of the circuit is **126 volts**.
\[
V = I \times R
\]
where \( V \) is the voltage, \( I \) is the current, and \( R \) is the total resistance in the circuit.
1. First, calculate the total resistance \( R \) in the circuit. In a series circuit, the total resistance is simply the sum of all individual resistances:
\[
R_{\text{total}} = R_1 + R_2 + R_3
\]
Given:
- \( R_1 = 10 \, \text{ohms} \)
- \( R_2 = 5 \, \text{ohms} \)
- \( R_3 = 6 \, \text{ohms} \)
Calculating the total resistance:
\[
R_{\text{total}} = 10 \, \text{ohms} + 5 \, \text{ohms} + 6 \, \text{ohms} = 21 \, \text{ohms}
\]
2. Now, use the total resistance and the given current to find the voltage:
Given:
- \( I = 6 \, \text{amps} \)
Calculate the voltage:
\[
V = I \times R_{\text{total}} = 6 \, \text{amps} \times 21 \, \text{ohms} = 126 \, \text{volts}
\]
Therefore, the voltage of the circuit is **126 volts**.