A resistor with R = 850 Ωis connected to the plates of a charged capacitor with capacitance C =

step 1 Part A of the given problem, the energy initially stored in the capacitor is given by U .N. is e

A resistor with R = 850 Ωis connected to the plates of a...

A resistor with $R =$ 850 $\Omega$ is connected to the plates of a charged capacitor with capacitance $C =$ 4.62 $\mu$F. Just before the connection is made, the charge on the capacitor is 6.90 mC. (a) What is the energy initially stored in the capacitor? (b) What is the electrical power dissipated in the resistor just after the connection is made? (c) What is the electrical power dissipated in the resistor at the instant when the energy stored in the capacitor has decreased to half the value calculated in part (a)?

Key Concepts

Capacitor Energy Storage

This concept involves the calculation of energy stored in a capacitor, which is defined by the equation U = 1/2 CV² or, equivalently, U = Q²/(2C) when the charge is used. Understanding how the energy depends on the capacitor's capacitance and the voltage (or charge) across it is essential for analyzing circuits where energy is stored and later released.

RC Circuit Transient Behavior

This concept refers to the analysis of circuits that include a resistor and capacitor (RC circuits), particularly their response when a capacitor discharges through a resistor. The discharging process follows an exponential decay law characterized by a time constant ? = RC. This behavior is crucial for predicting how voltages, currents, and stored energy change over time in transient states.

Electrical Power Dissipation in Resistors

This concept covers the way electrical energy is converted into heat in resistive components. In the context of RC circuits, the instantaneous power dissipated across a resistor can be calculated using expressions such as P = V²/R, where V is the voltage across the resistor, or P = I²R with the current through it. Understanding power dissipation is important for both energy considerations and thermal management in circuits.

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