In capacitor charging behavior, how is the time variation of voltage and current most accurately characterized for a simple RC network driven by a DC step?

Introduction:
This question tests core time-domain intuition for RC circuits. When a DC step is applied, the capacitor voltage and current follow characteristic curves governed by the RC time constant, revealing exponential charging and discharging behavior.

Given Data / Assumptions:

• Simple series RC circuit.
• Input is an ideal DC step applied at t = 0.
• Capacitor initially uncharged.
• Linear components and constant parameters R and C.

Concept / Approach:
The governing differential equation for a series RC with a DC step yields solutions of the form v_c(t) = V * (1 - exp(-t / (RC))) and i(t) = (V/R) * exp(-t / (RC)). Both voltage rise and current decay are exponential functions with time constant tau = RC.

Step-by-Step Solution:
1) Apply a DC step across the series RC.2) Current initially equals V/R and then decreases as charge accumulates on the capacitor plates.3) Capacitor voltage starts at 0 and asymptotically approaches V.4) The mathematical form for both is exponential with time constant tau = RC.

Verification / Alternative check:
Measuring voltage vs time on an oscilloscope for a DC step shows the familiar exponential approach to the final value. Fitting the curve yields tau that matches R*C.

Why Other Options Are Wrong:
Linear: would imply constant slope, which does not match RC dynamics.
Magnetic: relates to inductors, not capacitors, as the dominant effect.
A current block: capacitors pass transient current; they do not perfectly block current over time only at steady DC.
Logarithmic: does not match the solution of the first-order RC differential equation.

Common Pitfalls:
Assuming an immediate step in capacitor voltage, confusing steady-state DC blocking with transient behavior, or thinking the current stays constant. In reality the current decays exponentially as the capacitor charges.

Final Answer:
exponential