For a circuit with a capacitor C=1200uF, power supply 12V and resistor of 50 Kilo ohms, what are the following? A capacitor with C = 1200 μ F is fully charged using a 12 V power supply. At time t = 0, you start discharging the capacitor via a 50 kilo ohm resistor. Calculate the initial charge Qmax and the initial energy Emax stored in the capacitor. Express as decimal numbers with 2 significant figures.Calculate the residual charge Q, the potential difference V across the capacitor and its energy E content after 68 seconds. Express as decimal numbers with 2 significant figures
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When a capacitor is fully charged, the maximum energy stored is given by (1/2)*C*V^2, the maximum charge is Q = CV
As the capacitance C = 1200* 10^-6 F and the maximum voltage V = 12V
Qmax = 1200*10^-6 * 12 = 14.40 mC
Emax = (1/2)*1200*10^-6*12^2
=> (1/2)*1200*10^-6*144
=> 86.40 mJ
When a capacitor discharges:
the residual charge after time t is: C*V*e^(-t/RC)
substituting the values we have:
the residual charge Q
=> 1200* 10^-6 * 12*e^(-68/(1200* 10^-6*50*10^3))
=> 14400*10^-6* = 4.63 mC
the residual voltage V = 12 * e^(-68/(1200* 10^-6*50*10^3))
=> 3.86 V
The residual energy E is (1/2)*V*Q
=> (1/2)*4.63*3.86
=> 8.94 mJ
The required values are:
Qmax = 14.40 mC , Emax = 86.40 mJ, Q = 4.63 mC, V = 3.86 V and E = 8.94 mJ
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