Question

Please just look over my work to see if I have been doing the problems right. Also help me solve the table for the combined circuits. Please show your work and explain. Also help me fill in column L.

Error Analysis not needed. Assume the equivalent voltage is 14V and every light bulb is a 1 ohm resistor.

Label the brightness of the single bulb circuit (problem 1) as L=10. This light bulb will serve as a baseline for the experiment. If a bulb in another circuit is less bright than this bulb, label it with a brightness of less than 10. If a bulb is brighter label it with brightness greater than 10.

As the luminosity of the light was not measured with any certainty, error analysis will not be necessary in this assignment. For every circuit, assume the equivalent voltage is 14 V and that every light bulb is a 1 ohm resistor.

Answer 1

1) P = V^2 /R = 14^2 / 1 = 196 W
2) we have V = I * ( R1 + R2)
14= I * 2
I = 7 A
so, V in R1 = I * R = 7 V
P in R1 = I^2 * R1 = 49 W
so, L for R1 = 10 * 49/ (196) = 2.5
I in R2 = 7 A
V in R2 = I * R2 = 7 V
P in R2 = I^2 * R2 = 49 W
L for R2 = (10 * 49) / 196 = 2.5
Req = ( R1 + R2) = 2
we have I for Req = V/ Req = 14/2 = 7 A
V in Req = I * req = 7 * 2 = 14 V
P in Req = I^2 * Req = (7^2) * 2 = 98 W
L for Req = ( 10 * 98) / 196 = 5
3)
Voltage across R1 = 14 V
Current across R1 = 14/R1 = 14 A
Power , P in R1 = V^2 / R1 =14^2 = 196 W
L in R1 = (196 * 10)/196 = 10
Voltage across R2 = 14 V
Current across R2 = 14/R2 = 14 A
Power , P in R2 = V^2 / R2 =14^2 = 196 W
L in R2 = (196 * 10)/196 = 10
Req = 1/(( 1/R1) + (1/R2)) = 1/ ((1/1) + (1/1)) = 0.5 ohms
Voltage across Req = 14 V
Current across Req = 14/Req = 14/0.5 = 28 A
Power , P in Req = V^2 / Req =14^2/0.5 = 392 W
L in Req = (392 * 10)/196 = 20
4)
Current across R1 = 14/(R1 + R2 + R3) = 14/3 = 4.667 A
Voltage across R1 = I * R1 = 4.667 * 1 = 4.667 V
Power , P in R1 = V^2 / R1 =4.667^2 = 21.780889 W
L in R1 = (21.780889* 10)/196 = 1.111
Current across R2 = 14/(R1 + R2 + R3) = 14/3 = 4.667 A
Voltage across R2 = I * R2 = 4.667 * 1 = 4.667 V
Power , P in R2 = V^2 / R2 =4.667^2 = 21.780889 W
L in R2 = (21.780889* 10)/196 = 1.111
Current across R3 = 14/(R1 + R2 + R3) = 14/3 = 4.667 A
Voltage across R3 = I * R3 = 4.667 * 1 = 4.667 V
Power , P in R3 = V^2 / R3 =4.667^2 = 21.780889 W
L in R3 = (21.780889* 10)/196 = 1.111
Req = R1 + R2+ R3 = 3 ohms
Current across Req = 14/(R1 + R2 + R3) = 14/3 = 4.667 A
Voltage across Req = I * Req = 4.667 * 3 = 14 V
Power , P in Req = V^2 / Req =14^2/3 = 65.333 W
L in Req = (65.333* 10)/196 = 3.333
5)
Voltage across R1 = 14 V
Current across R1 = 14/R1 = 14 A
Power , P in R1 = V^2 / R1 =14^2 = 196 W
L in R1 = (196 * 10)/196 = 10
Voltage across R2 = 14 V
Current across R2 = 14/R2 = 14 A
Power , P in R2 = V^2 / R2 =14^2 = 196 W
L in R2 = (196 * 10)/196 = 10
Voltage across R3 = 14 V
Current across R3 = 14/R3 = 14 A
Power , P in R3 = V^2 / R3 =14^2 = 196 W
L in R3 = (196 * 10)/196 = 10
Req = 1/(( 1/R1) + (1/R2) + (1/R3)) = 1/ ((1/1) + (1/1) + (1/1)) = 0.333 ohms
Voltage across Req = 14 V
Current across Req = 14/Req = 14/0.333 = 42 A
Power , P in Req = V^2 / Req =14^2/0.333 = 588 W
L in Req = (588 * 10)/196 = 30
6)