2: Physics Experiment 9 Stpm Sem

[ V(t) = V_0 e^{-t/RC} ]

Introduction

A capacitor stores electrical energy in an electric field. When a charged capacitor discharges through a resistor, the potential difference ( V ) across the capacitor does not drop instantly to zero. Instead, it follows an exponential decay described by the equation: physics experiment 9 stpm sem 2

A well-conducted experiment yields a linear plot of ( \ln(V) ) vs. ( t ), confirming the exponential decay model. For instance, if the slope is found to be -0.095 s⁻¹, then ( τ = 1/0.095 ≈ 10.5 ) seconds. Comparing this experimental time constant with the theoretical value ( RC ) (e.g., 10 kΩ × 1000 µF = 10.0 s) gives a percentage error typically within 5–10%, depending on component tolerances and reaction time errors. Sources of discrepancy include the internal resistance of the voltmeter, leakage in the capacitor, and human latency in starting/stopping the stopwatch. [ V(t) = V_0 e^{-t/RC} ] Introduction A