The capacitor in the circuit shown below is initially uncharged. The switch is closed at t = 0 s. AVbattery = 30 V, C = 3.0 F, and R=2.0 Q. What is the current in the circuit at t = 7.5 s, in Ampere Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answe it is already given in the question statement. felt C
The capacitor in the circuit shown below is initially uncharged. The switch is closed at t = 0 s. AVbattery = 30 V, C = 3.0 F, and R=2.0 Q. What is the current in the circuit at t = 7.5 s, in Ampere Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answe it is already given in the question statement. felt C
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![The problem is about a circuit with a capacitor that is initially uncharged. The setup includes the following components:
- **Voltage Source (\(\Delta V_{\text{battery}}\))**: 30 V
- **Capacitance (C)**: 3.0 F
- **Resistance (R)**: 2.0 Ω
The switch in the circuit is closed at time \(t = 0\) seconds. The task is to find the current in the circuit at \(t = 7.5\) seconds.
**Diagram Explanation**:
The circuit diagram displays a series circuit comprising a battery, a resistor (R), a capacitor (C), and a switch. The resistor is shown as a zig-zag line, characteristic of resistor symbols. The capacitor is depicted as two parallel lines, slightly separated. When the switch (drawn as a break in the line) is closed, current flows from the battery through the resistor and the capacitor.
**Instructions for Answering**:
- The answer must include two significant figures.
- If the answer is negative, include the negative sign.
- No positive sign or unit is necessary in the answer.
This scenario involves finding the charging current in an RC circuit at a specific time after the switch is closed, which typically involves using the formula for the current in a charging RC circuit:
\[ I(t) = \frac{V}{R} \times e^{-\frac{t}{RC}} \]
Here, \(V\) is the battery voltage, \(R\) is the resistance, \(C\) is the capacitance, and \(t\) is the time after the switch is closed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb06f2f1-740c-4a3c-a772-d40c08df0c93%2F1fe90c51-66c6-47d2-958c-56d60150cb9f%2F3zc594f_processed.png&w=3840&q=75)
Transcribed Image Text:The problem is about a circuit with a capacitor that is initially uncharged. The setup includes the following components:
- **Voltage Source (\(\Delta V_{\text{battery}}\))**: 30 V
- **Capacitance (C)**: 3.0 F
- **Resistance (R)**: 2.0 Ω
The switch in the circuit is closed at time \(t = 0\) seconds. The task is to find the current in the circuit at \(t = 7.5\) seconds.
**Diagram Explanation**:
The circuit diagram displays a series circuit comprising a battery, a resistor (R), a capacitor (C), and a switch. The resistor is shown as a zig-zag line, characteristic of resistor symbols. The capacitor is depicted as two parallel lines, slightly separated. When the switch (drawn as a break in the line) is closed, current flows from the battery through the resistor and the capacitor.
**Instructions for Answering**:
- The answer must include two significant figures.
- If the answer is negative, include the negative sign.
- No positive sign or unit is necessary in the answer.
This scenario involves finding the charging current in an RC circuit at a specific time after the switch is closed, which typically involves using the formula for the current in a charging RC circuit:
\[ I(t) = \frac{V}{R} \times e^{-\frac{t}{RC}} \]
Here, \(V\) is the battery voltage, \(R\) is the resistance, \(C\) is the capacitance, and \(t\) is the time after the switch is closed.
Expert Solution
Step 1: Determine the given variables
Voltage, V = 30 V
C = 3 F
R = 2 ohm
Current at t = 7.5 s is to be calculated.
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