A second series RC circuit is analyzed. The resistance of the resistor is known

Question

A second series RC circuit is analyzed. The resistance of the resistor is known to be R? = 400 K Ohm, and the potential difference of the battery is V_0 = 4.0 V. This time, however, the capacitance of the capacitor is not known. A plot of the circuit charging and discharging is shown in Figure 7. The voltage across the capacitor was measured at the four times shown in the figure, and the measured voltages and corresponding times are given in the accompanying table. Use these data to compute the half time of the RC circuit three times, and find the average half time. Use the average half time to compute the capacitance of the capacitor.

Explanation / Answer

V= V0 exp(-t/RC)

when the volage reduces to half

V0/V = exp(t/RC) = 2

t (half) = 0.693*RC

the voltage reduced to half at each point from e to f,g and h

half time = 1.65-1.53 = 0.12 s

               = 1.80 - 1.65 = 0.15 s

                = 1.96 - 1.80 = 0.16 s

average half-time = (0.12+0.15+0.16)/3 = 0.143 s

0.693 RC = 0.143

R =400k ohms

C = 0.143/0.693*400e+3

     = 51.56 uF

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.