RC Circuits 5. The charge on a C = 0.4F capacitor is measured as a function of time in a physics lab and produces th following graph. The capacitor is part of a simple circuit having only a battery, a capacitor, and a resistor in series. The capacitor starts uncharged and at t3D0s, the battery is plugged in and the capacitor charges. In general, the charge of a charging capacitor is given by: q(t) = Qmax(1 – e-/RC) %3D тах
RC Circuits 5. The charge on a C = 0.4F capacitor is measured as a function of time in a physics lab and produces th following graph. The capacitor is part of a simple circuit having only a battery, a capacitor, and a resistor in series. The capacitor starts uncharged and at t3D0s, the battery is plugged in and the capacitor charges. In general, the charge of a charging capacitor is given by: q(t) = Qmax(1 – e-/RC) %3D тах
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![**RC Circuits**
6. The charge on a \( C = 0.4 \, \text{F} \) capacitor is measured as a function of time in a physics lab and produces the following graph. The capacitor is part of a simple circuit having only a battery, a capacitor, and a resistor in series. The capacitor starts uncharged and at \( t = 0 \, \text{s} \), the battery is plugged in and the capacitor charges. In general, the charge of a charging capacitor is given by:
\[
q(t) = q_{\text{max}} \left( 1 - e^{-t/RC} \right)
\]
**Graph: Charge vs. Time**
- The graph shows the charge (in Coulombs) on the y-axis versus time (in seconds) on the x-axis.
- The curve begins at the origin (0,0) and follows an exponential growth pattern, leveling off as it approaches a maximum charge around 20 Coulombs at 10 seconds.
**Questions:**
a. **Time Constant Estimation**
- Use the graph to estimate the time constant for this circuit, \( \tau \).
b. **Resistance Estimation**
- Estimate the resistance of the resistor \( R \) in this circuit.
c. **Battery Voltage Estimation**
- Estimate the battery’s voltage \( \Delta V \) in this circuit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb520c17-8305-428a-b4d1-cb4273cbb5b6%2Fe2a2bcc1-9502-4557-9c98-7a77b6c67948%2Flc5fcuv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**RC Circuits**
6. The charge on a \( C = 0.4 \, \text{F} \) capacitor is measured as a function of time in a physics lab and produces the following graph. The capacitor is part of a simple circuit having only a battery, a capacitor, and a resistor in series. The capacitor starts uncharged and at \( t = 0 \, \text{s} \), the battery is plugged in and the capacitor charges. In general, the charge of a charging capacitor is given by:
\[
q(t) = q_{\text{max}} \left( 1 - e^{-t/RC} \right)
\]
**Graph: Charge vs. Time**
- The graph shows the charge (in Coulombs) on the y-axis versus time (in seconds) on the x-axis.
- The curve begins at the origin (0,0) and follows an exponential growth pattern, leveling off as it approaches a maximum charge around 20 Coulombs at 10 seconds.
**Questions:**
a. **Time Constant Estimation**
- Use the graph to estimate the time constant for this circuit, \( \tau \).
b. **Resistance Estimation**
- Estimate the resistance of the resistor \( R \) in this circuit.
c. **Battery Voltage Estimation**
- Estimate the battery’s voltage \( \Delta V \) in this circuit.
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