2 What is the total energy dissipated in the resistor after

44. [2pt The circuit below was at position a for a long time. It is suddenly switche The circuit below was at position a for a long time. It is suddenly switche Tar aach ctatement select T True. F False)

Solution

Voltage Vo = 3volt

Resistance R = 300 ohm

Capacitance C = 3 x10 ^-6 F

Time t= 1.5 x10 ^-3 s

In the dischargeing of the capacitor in RC circuit,

Charge at time t is q = Q e ^-t/RC

Where Q = maximum charge

   qC = QC e ^-t/RC

We know qC = V and QC = Vo Where Vo = maximum voltage

Therefore V = Vo e -t/RC

                  = 3 e ^{-(1.5 x10^-3 )/(300)(6x10^-6)}

                 = 3 e ^-0.833

                 =3(0.4345)

                 =1.303 volt

(b).Total energy dissipated in the resistor P=Vo ²/R

                                                              = 3 ² / 300

                                                              = 0.03 watt

(c).

Time t= 1.1 x10 ^-3 s

In the dischargeing of the capacitor in RC circuit,

Charge at time t is q = Q[1- e ^-t/RC]

Where Q = maximum charge

   qC = QC [1-e ^-t/RC ]

We know qC = V and QC = Vo Where Vo = maximum voltage

Therefore V = Vo [1- e ^-t/RC]

                  = 3 [1- e ^{-(1.1 x10^-3 )/(300)(6x10^-6)} ]

                 = 3[1- e ^-0.833]

                 =3(1- 0.6111)

                 =3(0.3888)

                 = 1.1666 volt