Question
A series circuit contains three 2 Ω resistors and a 6 Ω resistor. The current in each resistor is 4.0 A.
What is the voltage of the battery in the circuit?
2.0 V
3.0 V
32 V
48 V
What is the voltage of the battery in the circuit?
2.0 V
3.0 V
32 V
48 V
Answers
Answered by
GPT-4o mini
In a series circuit, the total resistance can be calculated by adding the resistance values of all resistors. In this case, you have three 2 Ω resistors and one 6 Ω resistor.
Total resistance \( R_t \) can be calculated as follows:
\[
R_t = R_1 + R_2 + R_3 + R_4
\]
Where:
- \( R_1, R_2, R_3 \) are the 2 Ω resistors,
- \( R_4 \) is the 6 Ω resistor.
Calculating the total resistance:
\[
R_t = 2 Ω + 2 Ω + 2 Ω + 6 Ω = 12 Ω
\]
Now, to find the voltage \( V \) across the entire circuit, we can use Ohm's Law, which states that \( V = I \cdot R \), where:
- \( I \) is the current,
- \( R \) is the total resistance.
Given that the current \( I \) is 4.0 A:
\[
V = I \cdot R_t = 4.0 A \cdot 12 Ω = 48 V
\]
Therefore, the voltage of the battery in the circuit is **48 V**.
Total resistance \( R_t \) can be calculated as follows:
\[
R_t = R_1 + R_2 + R_3 + R_4
\]
Where:
- \( R_1, R_2, R_3 \) are the 2 Ω resistors,
- \( R_4 \) is the 6 Ω resistor.
Calculating the total resistance:
\[
R_t = 2 Ω + 2 Ω + 2 Ω + 6 Ω = 12 Ω
\]
Now, to find the voltage \( V \) across the entire circuit, we can use Ohm's Law, which states that \( V = I \cdot R \), where:
- \( I \) is the current,
- \( R \) is the total resistance.
Given that the current \( I \) is 4.0 A:
\[
V = I \cdot R_t = 4.0 A \cdot 12 Ω = 48 V
\]
Therefore, the voltage of the battery in the circuit is **48 V**.