Question

Problem 4 Capacitor Voltage (V) vs Time (s) 140 120 100 e 80 60 40 20 10 Time (s) 20 15 This graph shows the voltage across a discharging capacitor, which follows the rule: 1.) Using the information in the graph, what is the value of Vo? 10 2.) What is the halftime for the voltage decay (the time at which the voltage reaches half its initial value)? Read the value from the graph to the nearest whole number of seconds. 3.) Usjng the values of Vo, V Vo and ti/2 from question 2, find the time constant τ for this circuit. o We 4.) If the resistance is 6 M2 what is the value of the capacitance? *10

Answer 1

Capacitor Voltage (V) vs Time (s) 140 100. 80 60 40 20 4 10 15 20 Time (s)

1) The value of V₀ = 120 V

2) The time at which the voltage reaches half of its initial value i.e 60 V = 4 s

3) $V = V_0 e^{-t/\tau}$

60120e-4/

0.5 = e-47

Taking natural logarithm on both sides:

-0.693 =-4/T

т = 4/0.693 5.77s

4) We know $\tau = RC$

(6 × 10°)C 5.77

C= 9.6 × 10-1F= 0.96μ F