Charging a Capacitor in an RC Circuit (a) A capacitor in series with a resistor,

Question

Charging a Capacitor in an RC Circuit (a) A capacitor in series with a resistor, switch, and battery. (b) When the switch is thrown to position a, the capacitor begins to charge up. (c) When the switch is thrown to position b, the capacitor discharges An uncharged capacitor and a resistor are connected in series to a battery as shown in the figure, where = 12.0 V, C = 4.00 and R = 7.5 × 105 . The switch is thrown to position a. Find the time constant of the circuit, the maximum charge on the capacitor, the maximum current in the circuit, and the charge and current as functions of time SOLVE IT Conceptualize: Study the figure and imagine throwing the switch to position a as shown in Figure (b). Upon doing so, the capacitor begins to charge Categorize: We evaluate our results using equations developed in this section, so we categorize this example as a substitution problem

Explanation / Answer

a) new time constant = 8.4 * 10-6 * 2.386 * 105

                                  = 2 sec

b)   maximum current =   12/(2.386 * 105)

                                   =   5.029 * 10-5   A

c)   new time constant = 2.095 * 10-6 * 11* 105

                                  = 2.3045 sec

d)   maximum current =   12/(11 * 105)

                                   =   1.091 * 10-5   A

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