Physic Labs

Problem 2

A capacitor C charged to V₀ discharges through resistor R, with q(0)=CV₀. Find q(t) and discharge current i(t). Use the stated ideal model: quantities are constant or vary only as specified, with no extra drag, losses, or external influences. State a sign convention, keep units consistent, and use a classical approximation only where appropriate. (a) Set up the governing equation from a fundamental law. (b) Solve for the requested quantity under the stated conditions. (c) Check the result using a suitable limit, sign, or unit test, and report both the expression and its physical meaning.
iout(t)=−dq/dt=(V0/R)e−t/(RC)i_{\rm out}(t)=-dq/dt=(V_0/R)e^{-t/(RC)}
problems.proof.analysis

Check with an independent law, limiting case, or physical sign. This can expose a convention error and confirms that the linked parts use consistent data.