Question
charge Q coulombs at time t seconds is given by the differential equation RdQ/dt+Q/C=0, where c is the capacitance in farafd and R the resistance in ohms.solve the equation for Q given that Q=Qo where t=0
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plz show step plz plz plz
Answers
Steve
R dQ/dt + Q/C = 0
R dQ/dt = -Q/C
dQ/dt = -Q/(RC)
dQ/Q = -1/(RC) dt
lnQ = -1/(RC) t + k
at t=0, we know that Q=Qo, so
lnQo = k
so,
lnQ = -1/(RC) + lnQo
ln(Q/Qo) = -1/(RC) t
Q/Qo = e^(-t/RC)
Q = Qo e^(-t/RC)
R dQ/dt = -Q/C
dQ/dt = -Q/(RC)
dQ/Q = -1/(RC) dt
lnQ = -1/(RC) t + k
at t=0, we know that Q=Qo, so
lnQo = k
so,
lnQ = -1/(RC) + lnQo
ln(Q/Qo) = -1/(RC) t
Q/Qo = e^(-t/RC)
Q = Qo e^(-t/RC)