Please solve all parts (1) What is the current through each resistor, and what i
ID: 2304800 • Letter: P
Question
Please solve all parts (1) What is the current through each resistor, and what is the power delivered to Ry? 4.00 ? E3 70.0 V 60.0 V 80.0 V Clicker Questions: (iii) 13 ; (iv) P- w R2 3.00 m (2.b) This circuit has junctions, which means you'll need to equation(s)? This circuit has 2.00 ? junction rule Ri loops, which means you'll need to compose loop rule equation(s) (3) Compose a junction rule equation for junction c, labeling currents according to the resistor they will go through. For example Is is the c junction c: Check: Is this the same equation, mathematically, as that for junction f? (4) Compose loop rule equations. (There are three possible loops in this circuit; you only need two to Gunc) solve the problem.) loop abcfa.: loop edcfe: loop edcbafe:: (5) You now have three equations [(1). (2) and (3), above] and three unknowns: Ii, /2, and Is. Make 0 (2) 50 (3) -0 (extra) a plan to reduce this system to two equations and two unknowns on your way to solving for the first of the variables. Check: Check your work by assessing the values of I and Js in the "extra" loop equation.
Explanation / Answer
1. let current I leave E1 +ve terminal
i leave E2
tthen from juction equation
I + i goes into E3
hence
using kirchoff's loop laws
E1 = E2 - iR2 + IR1
E1 = (i + I)R3 + E3 + IR1
now
E1 = 70 V
E2 = 60 V
E3 = 80 V
R1 = 2 ohm
R2 = 3 ohm
R3 = 4 ohm
hence
70 = 60 - 3i + 2I
2I - 3i = 10
70 = (i + I)4 + 80 + 2I
6I + 4i = -10
8I + i = 0
i = -8I
hence
6I - 32I = -10
-26I = -10
I = 10/26 A
i = -80/26 A
hence
i + I = -70/26 A
i) I1 = I = 10/26 A
ii)I2 = i = -80/26 A
iii) I3 = -70/26 A
iv) P1 = I1^2*R1 = 0.2958579881656 W
2.b this circuit has two junctinos, so it will have two junction rule equations
3. for junction c
i1 + i2 = i3
for junction f
i1 + i2 = i3
hence its numerically the same equation
4. for loop abcfa
E1 = E2 - 3I2 + 2I1
for loop edcfe
E3 = -4I3 + E2 - 3I2
for loop edcbafe
E3 = -4I3 + E1 - 2I1
5) solving we get
i) I1 = I = 10/26 A
ii)I2 = i = -80/26 A
iii) I3 = -70/26 A