A student makes a homemade resistor from a graphite pencil 5.00 cm long, where the graphite is 0

step 1 Now to first start off the question to find the RC constant, we need both the resistance as well

A student makes a homemade resistor from a graphite pencil...

A student makes a homemade resistor from a graphite pencil $5.00 \mathrm{cm}$ long, where the graphite is $0.05 \mathrm{mm}$ in diameter. The resistivity of the graphite is $\rho=1.38 \times 10^{-5} \Omega / \mathrm{m} .$ The homemade resistor is place in series with a switch, a 10.00 -mF capacitor and a 0.50 -V power source. (a) What is the $R C$ time constant of the circuit? (b) What is the potential drop across the pencil 1.00 s after the switch is closed?

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Key Concepts

Resistivity and Resistance Calculation

Resistivity is an intrinsic property of a material that quantifies how strongly the material opposes the flow of electric current. When calculating resistance, the formula R = ?L/A is used, where ? is the resistivity, L is the length of the conductor, and A is its cross-sectional area. This concept is fundamental in understanding how the dimensions and material properties affect the overall resistance in any resistor.

RC Circuit and Time Constant

An RC circuit consists of a resistor and a capacitor connected in series, and its behavior is characterized by a time constant ?, which is the product of the resistance (R) and the capacitance (C). The time constant is a measure of the rate at which the capacitor charges or discharges, and it plays a crucial role in analyzing the transient response of the circuit.

Exponential Charging of a Capacitor

The charging process of a capacitor in an RC circuit follows an exponential behavior described by the equation V(t) = V_source (1 - e^(-t/?)), where V(t) is the voltage across the capacitor at time t, V_source is the applied voltage, and ? is the RC time constant. This exponential function is key to predicting how the voltage changes over time as the capacitor charges.

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