i. A 55.0 to a capacitor initially charged to a voltage of v is connected to a 1
ID: 1446333 • Letter: I
Question
i. A 55.0 to a capacitor initially charged to a voltage of v is connected to a 100 k resistor as shown. a) What is the voltage on the capacitor 10.o seconds after the switch is thrown? b) The capacitor is reasonably safe when the voltage drops to 48.0v. How long after the switch is thrown does it take for the voltage to drop to this reasonably safe level? 2. An electron, me 9.11x10 31 kg, moves with a speed of 1000 m/s in the plane of the paper as shown. It enters a uniform 8.00 T magnetic field that is perpendicular to the paper as drawn. 50° a) On the diagram sketch the path of the electron inthe field. b) What is the radius of the electron's path?Explanation / Answer
1) The voltage across the capacitor after t seconds is
Vc = V e-t/RC --------------- 1
where Vc is the voltage across the capacitor at the time t s , V is the initial voltage ,R and C are the resistance and the capacitance respectively
Voltage on the capacitor after 10s
Vc = 900 x e-10 /100 k x 55uF
= 817 v
b) Rearrange equation 1
t = RC ln ( V/Vc )
t = 100 x 103 x 55 x 10-6 x ln(900 / 48 )
t = 16.12 s
2 The electron will follow a circular path
b )
Even though the electron enters the plane with an angle ,it is perpendicular to the magnetic field
the radius of the circular path is
r = m v / e B
Where m is the mass of the electron , v is the velocity with which it enters , e is the charge of the electron ,B is the magnetic field
r = 9.11 x 10-31 x 1000 / 1.6 x 10-19 x 8
r = 7.11 x10-10m
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