An aerospace technician is testing a backup capacitor system designed for an emergency landing gear mechanism. The capacitor discharges through an actuator circuit of constant resistance. The technician measures the time t0.5t_{0.5}t0.5 for the potential difference across the capacitor to fall to half of its initial fully-charged value. Five independent trials of this measurement yield the following results:
18.64 s,18.42 s,18.78 s,18.50 s,18.91 s 18.64\text{ s}, \quad 18.42\text{ s}, \quad 18.78\text{ s}, \quad 18.50\text{ s}, \quad 18.91\text{ s} 18.64 s,18.42 s,18.78 s,18.50 s,18.91 sDetermine the percentage uncertainty in the measurement of t0.5t_{0.5}t0.5.
Calculate the time constant τ\tauτ for this discharge circuit.
