A 2.00 -nF capacitor with an initial charge of 5.10 μC is discharged through a 1.30-k Ωresistor.

step 1 So we're giving some information about an RC circuit, and we're told that a capacitor is being d

A 2.00 -nF capacitor with an initial charge of 5.10 μC is...

A 2.00 -nF capacitor with an initial charge of $5.10 \mu \mathrm{C}$ is discharged through a $1.30-\mathrm{k} \Omega$ resistor. (a) Calculate the current in the resistor $9.00 \mu \mathrm{s}$ after the resistor is connected across the terminals of the capacitor. (b) What charge remains on the capacitor after $8.00 \mu \mathrm{s} ?$ (c) What is the maximum current in the resistor?

Key Concepts

Exponential Decay

Exponential decay describes the mathematical behavior of the voltage, charge, and current in a discharging RC circuit. The relationships are governed by an exponential function, where the magnitude of these quantities decreases over time as e to the power of negative time divided by the time constant. This decay behavior is crucial for predicting circuit behavior at any moment during the discharge process.

Initial Conditions

Initial conditions, such as the initial charge or voltage on the capacitor, are necessary to determine the subsequent behavior of an RC circuit. In the analysis of discharging circuits, the initial conditions set the starting point for the exponential decay and are used to calculate how the current and charge evolve over time, including determining maximum or peak current values.

RC Circuit

An RC circuit consists of a resistor (R) and a capacitor (C) connected in series or parallel. In a discharging RC circuit, the capacitor releases its stored energy through the resistor, and the voltage and current in the circuit decrease over time. This type of circuit is fundamental in electronics and is used in timing, filtering, and transient response applications.

Time Constant

The time constant, represented by the symbol ? (tau), is the product of resistance (R) and capacitance (C) in an RC circuit (? = RC). It characterizes the rate at which the capacitor charges or discharges; specifically, after a time period equal to ?, the voltage or charge on the capacitor falls to about 37% of its initial value during discharge.

Transcript

Please give Ace some feedback