An RC circuit is made from a 12 Volt battery, a 100 Ohm resistor, and a 250 mu F

Question

An RC circuit is made from a 12 Volt battery, a 100 Ohm resistor, and a 250 mu F capacitor connected in series. a) Find the time constant for the circuit. b) Find the maximum charge on the capacitor after the capacitor has charged. c) What is the energy stored in the capacitor once fully charged? d) When, in seconds, is the charge one-half the maximum charge? Prove that the voltage in a charging RC circuit will reach one-half the battery voltage in a time given by t_1/2 = RC In (2). A charged particle q= l times 10^-7 Coulombs moving at 200 m/s left to right enters a 0.10 Tesla magnetic field directly vertically out of the page as shown (fig. 3). Find the magnitude and the direction of the force on the particle as it enters the field. A proton, m = 1.67 times l0^-27 kg, in the solar wind takes 3 days to reach the earth from the sun 149 million kilometers away. It strikes the earth's magnetic field, approximately 5 times 10^-5 T in strength, and gets trapped into a circular cyclotron orbit. a) Estimate the velocity of the proton from the travel time from the sun to the earth. b) Find the radius of the cyclotron orbit in meters for the velocity in part a. c) Find the cyclotron time in seconds. d) How much work is done on the proton by the magnetic field while the particle is trapped in its cyclotron orbit? Briefly justify your answer. A wire with legs 5 cm long with a transverse section 2.5 cm long is immersed in a uniform 0.075 Tesla magnetic field as shown in figure 5. If a current of 4 Amperes is sent through the wire, a) Find the net magnetic force on the wire. b) What is the direction of the magnetic force on the wire?

Explanation / Answer

1)(a)Time constant of a RC circuit is given by

T = RC

T = 100 x 250 x 10^-6 = 0.025 s = 25 ms

Hence, T = 0.025 s = 25 ms

b)Q = CV

Q = 250 x 10^-6 x 12 = 3000 micro C

Hence, Q(max) = 3000 uC

c)U = 1/2 CV^2

U = 0.5 x 250 x 10^-6 x 12^2 = 0.018 J

Hence, U = 0.018 J = 18 mJ

d)Q' = Qm/2

we know that,

Q = Q (1 - e^-t/RC)

0.5 = 1 - e^-t/RC

e^-t/RC = 0.5

taking natural log both sides

-t/RC = -0.693

t = 0.693 x RC = 0.693 x 100 x 250 x 10^-6 = 0.0173 s

Hence, t = 0.0173 s = 17.3 ms

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