Answer:
Step-by-step explanation:
Given that,
Capacitance of capacitor
C = 151 nF
Resistance of a resistor
R = 10×10^6 ohms
Battery EMF
V = 9V
Charge on capacitor after t = 1.3sec?
This is an RC series circuit
Current in the circuit is given as
i= dq/dt
dq = i•dt
q = ∫i•dt
The voltage in the capacitor is give as
q = CV
Vc = q/C, since q = ∫i•dt
Vc = 1/C ∫i•dt
Therefore applying KVL
Vr + Vc = V.
Vr is voltage across resistor = iR
iR + 1/C ∫i•dt = V
Note that, i=dq/dt and q = ∫i•dt
R dq/dt + q/C = V
Solving this differential equation
Divide through by R
dq/dt + q/RC = V/R
Since, R = 10×10^6 C = 151×10^-9F
Then, dq/dt + q/RC = V/R
dq/dt + q/10×10^6 × 151×10^-9= 9/10×10^6
dq/dt + 0.662q = 9×10^-7
Using integrating factor method
IF = e(0.662t)
So,
q•e(0.662t) = 9×10^-7∫(e(0.662t)dt
q•e(0.662t) = 9 × 10^-7•e(0.662t) / 0.662 + K
q•e(0.662t)=1.36×10^-7•e(0.662t) + K
Divide through by e(0.662t)
q = 1.36×10^-7 + K•e(-0.662t)
At the beginning, there was no charge on the capacitor
q(0) = 0
0 = 1.36 × 10^-7 + k
Then, k = -1.36 ×10^-7
q =1.36×10^-7—1.36×10^-7•e(-0.662t)
Now, at t = 1.3s
q=1.36×10^-7— 1.36 ×10^-7•e(-0.662 × 1.3)
q=1.36×10^-7-1.36×10^-7•e(-0.8606)
q =1.36×10^-7—5.75 × 10^-8
q = 7.85 × 10^-8
Then, q = 78.5 nC