Set up the necessary and sufficient equations to solve (not necessary to solve t
ID: 1455921 • Letter: S
Question
Set up the necessary and sufficient equations to solve (not necessary to solve the equations for full credit) the circuit below for the currents. Assume all voltages are 200 V, and R_1 = 4 Ohm, R_2 = 6 Ohm, R_3 = 2 Ohm, R_4 = 2 Ohm and R_5 = 10 Ohm. A proton moves with a speed of 8.0 Times 10^6 m/s along the +x axis. It enters a region where there is Q a magnetic field of magnitude 3T directed at an angle of 300 degree to the +x-axis and lying in the x-y plane. Calculate the initial magnetic force on the proton.Explanation / Answer
Apply kirchoff's second law to left loop you get ,
200 = i3R5 +i1R2+i1R1
= 10 i3 +6i1 +4 i1
= 10 i3 +10 i1
20 = i3+i1 -------( 1)
Apply Kirchoff's second law to right loop you get ,
200 -200 = i2 R3 +i2 R4 -i3R5
0 = 2i2 +2i2 -10i3
0 = 4i2 -10 i3 -----------( 2)
From Kirchoff's first law , i1 =i2+i3
i2 = i1-i3
Substitute this in equation(2) you get ,
0 = 4(i1-i3) -10 i3
= 4i1 -14i3
4i1 = 14 i3
i1 = (14/4)i3 --------( 4)
Substitute this in equation( 1) you get,
20 = i3+(14/4)i3
= i3+3.5i3 = 4.5i3
from this i3 = 20 /4.5
= 4.44444 A
From equation(4) , i1 =(14/4)i3
= 15.5555A
We know i1 = i2 +i3
i2 = i1-i3
= 15.5555-4.4444
= 11.1111A
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