Marcia is an electrical engineer who is testing the voltage of a circuit given a certain current and resistance. She uses the following formula to calculate voltage: voltage = (current)-(resistance) The circuit she tests has a current of $$ 5+j 3 $$ amps and a resistance of $$ 3- $$ What is the voltage of the circuit? $$ 11+j $$ volts $$ 21+j $$ volts $$ 11-j $$ volts $$ 21-j $$ volts

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UpStudy AI · Accepted Answer

To determine the voltage in the circuit, let's clarify and follow the given information step by step.

### Given:
- **Current ($$ I $$)**: $$ 5 + j3 $$ amps
- **Resistance ($$ R $$)**: $$ 3 - j2 $$ ohms *(Assuming the resistance is $$ 3 - j2 $$ based on the provided options)*

**Note:** In electrical engineering, the standard formula to calculate voltage ($$ V $$) is Ohm's Law:
$$ V = I \times R $$

However, the problem states that Marcia uses:
$$ \text{Voltage} = \text{Current} - \text{Resistance} $$
This seems unconventional, but given the context and the multiple-choice options, we'll proceed under the assumption that the resistance is $$ 3 - j2 $$ ohms and apply the standard Ohm's Law.

### Calculation Using Ohm's Law:
$$ V = (5 + j3) \times (3 - j2) $$

Let's perform the multiplication:
$$
\begin{align*}
V &= 5 \times 3 + 5 \times (-j2) + j3 \times 3 + j3 \times (-j2) \
&= 15 - j10 + j9 - j^2 6 \
&= 15 - j10 + j9 + 6 \quad (\text{since } j^2 = -1) \
&= 21 - j \quad (\text{combining like terms})
\end{align*}
$$

### Final Answer:
The voltage of the circuit is **$$ 21 - j $$ volts**.

**Correct Option:**
- $$ \mathbf{21 - j} $$ volts
The voltage of the circuit is $$ 21 - j $$ volts.

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