Question
To measure the capacitance $C$ of a capacitor, you attach the capacitor to a battery and wait until it is fully charged. You then disconnect the capacitor from the battery and let it discharge through a resistor of resistance $R$. You measure the time $T_{1 / 2}$ that it takes the voltage across the resistor to decrease to half its initial value at the instant that the connection to the capacitor is first completed. You repeat this for several different resistors. You plot the data as $T_{1 / 2}$ versus $R$ and find that they lie close to a straight line that has slope $5.00 \mu \mathrm{F}$. What is the capacitance $C$ of the capacitor?
Step 1
Step 1: The current flowing in the circuit when the switch is closed is given by $I = \frac{E}{R} e^{-t/RC}$, where $E$ is the initial voltage across the capacitor, $R$ is the resistance, $C$ is the capacitance, and $t$ is the time. Show more…
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To measure the capacitance C of a capacitor, you attach the capacitor to a battery and wait until it is fully charged. You then disconnect the capacitor from the battery and let it discharge through a resistor of resistance RR. You measure the time T1/2 that it takes the voltage across the resistor to decrease to half its initial value at the instant that the connection to the capacitor is first completed. You repeat this for several different resistors. You plot the data as T1/2 versus R and find that they lie close to a straight line that has slope 9.00 μF. What is the capacitance C of the capacitor?
You measure the capacitance $C_{1}$ of a capacitor by doing the following: First connect capacitors $C_{1}$ and $C_{2}$ in series to a power supply that provides a voltage $V$ that can be varied. The capacitance of $C_{2}$ is known to be $3.00 \mu \mathrm{F}$. Then vary the applied voltage $V,$ and for each value of $V$ measure the voltage $V_{2}$ across $C_{2}$. After plotting your data as $V_{2}$ versus $V,$ you find that the data fall close to a straight line that has slope $0.650 .$ What is the capacitance $C_{1} ?$
You measure the capacitance C1 of a capacitor by doing the following: First, connect capacitors C1 and C2 in series to a power supply that provides a voltage V that can be varied. The capacitance of C2 is known to be 5.00 μF. Then vary the applied voltage V, and for each value of V, measure the voltage V2 across C2. After plotting your data as V2 versus V, you find that the data fall close to a straight line that has a slope of 0.450. What is the capacitance C1?
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