Time constant concept for RC networks.

Time constant concept for RC networks.

• A. The time constant is RC; roughly five time constants characterize near-final value.
• B. The time constant is the sum of R and C.
• C. The time constant equals R divided by C.
• D. The time constant equals C divided by R.

Answer: (A)

The time constant in an RC network is the product of resistance and capacitance, tau = R × C. This single value sets how fast the capacitor charges or discharges: the capacitor voltage follows an exponential behavior, with V(t) = V_final[1 − e^(−t/(RC))] during charging and V(t) = V_initial e^(−t/(RC)) during discharging. Because e^(−5) ≈ 0.0067, after about five time constants the transient is essentially finished and the voltage is very close to its final value. So stating that the time constant is RC and that roughly five time constants characterize the near-final value captures both the rate and a practical convergence criterion. The other options don’t fit because they propose sums or divisions that don’t reflect the actual time scale and would have the wrong units (sum is not dimensionally meaningful; R/C or C/R would yield units that aren’t seconds and do not describe the charging/discharging rate).

The time constant in an RC network is the product of resistance and capacitance, tau = R × C. This single value sets how fast the capacitor charges or discharges: the capacitor voltage follows an exponential behavior, with V(t) = V_final[1 − e^(−t/(RC))] during charging and V(t) = V_initial e^(−t/(RC)) during discharging. Because e^(−5) ≈ 0.0067, after about five time constants the transient is essentially finished and the voltage is very close to its final value. So stating that the time constant is RC and that roughly five time constants characterize the near-final value captures both the rate and a practical convergence criterion. The other options don’t fit because they propose sums or divisions that don’t reflect the actual time scale and would have the wrong units (sum is not dimensionally meaningful; R/C or C/R would yield units that aren’t seconds and do not describe the charging/discharging rate).