Capacitors are used in many applications where one needs to...

Capacitors are used in many applications where one needs to supply a short burst of relatively large current. A $100.0 \mu \mathrm{F}$ capacitor in an electronic flash lamp supplies a burst of current that dissipates $20.0 \mathrm{J}$ of energy (as light and heat) in the lamp. (a) To what potential difference must the capacitor initially be charged? (b) What is its initial charge? (c) Approximately what is the resistance of the lamp if the current reaches $5.0 \%$ of its original value in $2.0 \mathrm{ms} ?$

Capacitors are used in many applications where one needs to supply a short burst of relatively large current. A $100.0 \mu \mathrm{F}$ capacitor in an electronic flash lamp supplies a burst of current that dissipates $20.0 \mathrm{J}$ of energy (as light and heat) in the lamp.
(a) To what potential difference must the capacitor initially be charged?
(b) What is its initial charge?
(c) Approximately what is the resistance of the lamp if the current reaches $5.0 \%$ of its original value in $2.0 \mathrm{ms} ?$

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Key Concepts

Capacitor Energy Storage

This concept involves the energy stored in a capacitor, which is given by the formula E = ½ C V². It relates the energy (E) stored to the capacitance (C) and the potential difference (V) across the capacitor, making it possible to calculate how much voltage is needed for a given energy storage or vice versa.

Charge-Voltage-Capacitance Relationship

This concept is defined by the equation Q = C × V, where Q is the charge stored on the capacitor, C is the capacitance, and V is the voltage across it. This fundamental relationship links electrical charge to the energy storage properties of capacitors and is essential for determining the initial charge when the voltage is known.

RC Circuit Exponential Decay

In an RC circuit, when a charged capacitor discharges through a resistor, the voltage and the current decay exponentially over time according to the formulas V(t) = V0 exp(-t/RC) and I(t) = I0 exp(-t/RC). This concept explains how the time constant, ? = RC, governs the rate of decay, allowing one to determine the resistance when the decay in current (or voltage) over a known time interval is given.

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