Voltage Capacitor Analysis Report

Part-3
a(i) Decay of voltage across the capacitor is given by:
V = 200t0.5
Plotting graph based on the relation between voltage and time:
Time (sec) 1 2 3 4 5 6
Voltage 200 282.842 346.41 400 447.213 489.89
1 2 3 4 5 6
0
100
200
300
400
500
600
Time (sec)
Voltage
Voltage vs. Time graph
a(ii) Rate of change of voltage after 2 sec:
Rate of change = ∆ V
∆ t
Taking intervals between 2 and 3 sec
Rate of change of voltage = 346.41−282.842
2−3 = 63.568 Vol/sec

a(iii) Verification by calculus method:
V = 200t0.5
Rate of change of voltage w.r.t. time
dV
dt = 200
2 √ t
After 2 sec dV
dt = 200
2 √ t = 100
√2 = 70.71
There is error in solving by graph because graph interpolates linearly but the equation is non-
linear.
b) Equation of electrical charging by capacitor:
I = A (1.75 – e-t/3)
By the equation given above we can draw table:
Time 1 2 3 4 5 6 7 8 9 10
Current 1.04A 1.23
A
1.38A 1.48A 1.56A 1.61A 1.65A 1.68A 1.7
A
1.72A
1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2