RC Circuit Help

Question

Use the equation v_c= V(1-e^-t/RC)

 

to prove that when power supply is turned on

 

τ = t / (ln(V) - ln (V- v_c)

Answer 1

V_c = V(1 - e^-t/RC)

 

Now τ = RC, so solve for RC:

 

V_c/V = 1 - e^-t/RC

 

1 - V_c/V  = (V- V_c)/V =  e^-t/RC

 

ln[(V- V_c)/V] = -t/RC

 

Now ln(a/b) = ln a - ln b.  So:

 

ln((V-V_c) - ln(V) = -t/RC

 

RC = τ = t/(ln(V) - ln(V-V_c))