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LEARN MORE REMARKS Part (a) shows how useful information can often be obtained even when no details concerning capacitances, resistances, or voltages are known. Part (c) demonstrates that capacitors can be rapidly discharged (or conversely, charged), despite the mathematical form of the equations used, which indicate an infinite time would be required. QUESTION Suppose the initial voltage used to charge the capacitor were doubled. The time required for discharging all but the last quantum of charge would: increase. decrease. remain the same. PRACTICE IT Use the worked example above to help you solve this problem. Consider a capacitor C being discharged through a resistor R as shown in figure a. The initial potential difference across the capacitor is 24.0 V, the capacitance is 3.70 × 10?? F, and the resistance is 2.30 ?. (a) How long does it take for the charge on the capacitor to drop to one-fourth of its initial value? Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. s (b) Compute the initial charge and time constant. Q = 8.88e-5 C r = 8.51e-6 s (c) How long does it take to discharge all but the last quantum of charge, 1.6 × 10?¹? C? (Assume an exponential decrease during the entire discharge process.) 2.89e-4 s

          LEARN MORE
REMARKS Part (a) shows how useful information can often be obtained even when no details concerning capacitances, resistances, or voltages are known. Part (c) demonstrates that capacitors can be rapidly discharged (or conversely, charged), despite the mathematical form of the equations used, which indicate an infinite time would be required.
QUESTION Suppose the initial voltage used to charge the capacitor were doubled. The time required for discharging all but the last quantum of charge would:
increase.
decrease.
remain the same.
PRACTICE IT
Use the worked example above to help you solve this problem. Consider a capacitor C being discharged through a resistor R as shown in figure a. The initial potential difference across the capacitor is 24.0 V, the capacitance is 3.70 × 10?? F, and the resistance is 2.30 ?.
(a) How long does it take for the charge on the capacitor to drop to one-fourth of its initial value?
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. s
(b) Compute the initial charge and time constant.
Q = 8.88e-5 C
r = 8.51e-6 s
(c) How long does it take to discharge all but the last quantum of charge, 1.6 × 10?¹? C? (Assume an exponential decrease during the entire discharge process.)
2.89e-4 s

LEARN MORE
REMARKS Part (a) shows how useful information can often be obtained even when no details concerning capacitances, resistances, or voltages are known. Part (c) demonstrates that capacitors can be rapidly discharged (or conversely, charged), despite the mathematical form of the equations used, which indicate an infinite time would be required.
QUESTION Suppose the initial voltage used to charge the capacitor were doubled. The time required for discharging all but the last quantum of charge would:
increase.
decrease.
remain the same.
PRACTICE IT
Use the worked example above to help you solve this problem. Consider a capacitor C being discharged through a resistor R as shown in figure a. The initial potential difference across the capacitor is 24.0 V, the capacitance is 3.70 × 10?? F, and the resistance is 2.30 ?.
(a) How long does it take for the charge on the capacitor to drop to one-fourth of its initial value?
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. s
(b) Compute the initial charge and time constant.
Q = 8.88e-5 C
r = 8.51e-6 s
(c) How long does it take to discharge all but the last quantum of charge, 1.6 × 10?¹? C? (Assume an exponential decrease during the entire discharge process.)
2.89e-4 s

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