Question

enter the spectrometer. How close to the detector slit will they impact? 3. (a) What is the current through R? DATA: R = R2 R3= 15.0 22. V1 = 12.0 Volts. V2 = 3V1. (b) What is the current through R? (c) What is the current through Rz? detectors X X X X Fig. 1 Fig. 2 Fig. 3

Answer 1

Current through R1 , upward = i1

Current through R2, downward = i2

Current through R3, downward = i3

Using kirchoff's junction law

i1 = i3 + i2 eq(1)

Now using kirchoff's voltage law in left loop

V1 = i1*R1 + i2*R2

12 = 15.0*i1 + 15.0*i2
i1 + i2 = 12/15.0

i1 + i2 = 0.8 eq(2)

Now using kirchoff's voltage law in right loop

V2 = -i2*R2 + i3*R3

3*12 = -15*i2 + 15*i3

i3 - i2 = 3*12/15

i3 - i2 = 2.4 eq(3)

Now we have three equation and three unknowns, Solving these equations:

i1 = i3 + i2

i1 + i2 = 0.8

i3 - i2 = 2.4

Solving above three equation

i1 + i2 = 0.8

(i1 - i2) - i2 = 2.4

i1 - 2*i2 = 2.4

By subtracting,

3*i2 = -1.6

i2 = -1.6/3 Amp

i2 = -0.533 Amp

Which gives

i1 = 2*(-0.533) + 2.4 = 1.334 Amp

i3 = 1.334 - (-0.533) = 1.867 Amp

To check, apply voltage law across whole loop

V1 + V2 = i1*R1 + i3*R3

12 + 36 = 1.334*15 + 1.867*15

48 = 48.0

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