Homework SourseA circuit is constructed with four resistors one capacitor o
A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 59 , R3 = 48 and R4 = 93 . The capacitance is C = 49 F and the battery voltage is V = 24 V.
1)
The switch has been open for a long time when at time t = 0, the switch is closed. What is I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?
A
2)
What is I1(), the magnitude of the current that flows through the resistor R1 a very long time after the switch has been closed?
A
3)
What is Q(), the charge on the capacitor after the switch has been closed for a very long time?
C
4)
Consider the circuit above, with R5 = 83 in series with the capacitor. Once again, the switch has been open for a long time when at time t = 0, the switch is closed. What is I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?
A
5)
Continuing with the new circuit, what is Q(), the charge on the capacitor after the switch has been closed for a very long time?
C
Solution
1)
the equivalent resistance when switch is closed at t=0
[capacitor acts as short circuit]:
Req =R1+R4 =59+93 =152
current: I1(0)=V/Req = 24/152 = 0.158 A
2)
after long time capacitor acts as open circuit ,
thus the equivalent resistance:
Req= R1+R2+R3+R4 =78+78+67+62 = 259
current: I1(inf) =V/Req = 24/259 = 0.09266 A
3)
potential difference: V(inf) = I(inf)*(R2+R3) = 0.09266*(59+48) = 9.915 V
charge: Q(inf)= C*V(inf) = 49 uF*9.915 = 485.84 uC
4)
If the switch is closed at t=0 ,capacitor acts as short circuit ,
so equivalent resistance is,
Req = R1+R4+(R5||(R2+R3) =78+62+(83*107/83+107) = 198.74
current: I1(0) =V/Req = 24/198.74 = 0.1207 A
5)
the equivalent resistance:
Req=R1+R2+R3+R4 = 259
current: I1(inf) =V/Req =24/259 = 0.09266 A
potential difference:
V(inf)= I1(inf)*(R2+R3+R5) = 0.09266*(59+48+83) =17.6 V
charge: Q(inf)= C*V(inf) = 49 uF*17.6 = 862.7 uC
