Answer to Question #154058 in Differential Equations for Nouman Asghar Baig

Question

 Considering the LRC series with a charge of 𝛼 Henry, capacitance 0.000𝛽Farad, having the resistance of 50 times (𝛼 + 𝛽)ohms with emf of 100V. Suppose that no charge and current is present at time 𝑡 = 0 when the emf is applied. Determine the charge and current at any time 𝑡. Where 𝛼 and 𝛽 are the non zero digits of your registration number, 𝛼 being the tenth place digit and 𝛽 being the unit place digit. If 𝛼 or 𝛽 is zero then take any non-zero digit of your registration number. my reg no is 1 and 8

Answer 1

$q=\int_0^T c\epsilon (1-e^{\frac{-t}{Rc}})dt=c\epsilon t+Rce^{\frac{-t}{Rc}}|_0^T=c\epsilon T+Rce^{\frac{-T}{Rc}}+Rc$

c=0.0008 Farad

$\epsilon =100V$

R= 8.3145 J mol^-1K^-1

$q=0.0008(100T+8.3145e^{\frac{-T}{8.3145 x 0.0008}} + 8.3145)$

$\alpha= 1 Henry$ 

r=50(1+8)=450 ohms

$I=\int_0^Te^\frac{-rt }{\alpha}dt=\frac{-\alpha}{r}e^\frac{-rt }{\alpha}|_0^T=\frac{-1}{450}e^{-450T }-\frac{1}{450}=\frac{-1}{450}(e^{-450T }+1)$