1. IB 5.2 p225 #24
Copy the diagram
ID number of currents – Choose a direction for current with largest battery. Then follow that current and label all other currents until all have been identified.
For this problem, we know the current in the bottom loop is zero, so there is only one current, I for the top loop.
Write Kirch loop for top loop.
Counting CCW starting at battery
0 = For going over battery in same direction as current
– I(R1+R2) because the entire bar is part of the loop.
Solve this equation for I.

2. IB 5.2 p225 #24 Write Kirch loop for bottom loop.
There’s no current in this loop, so there is no forward and backward.
For counting purposes you can use either current direction.
For current through battery “properly” and counting CW starting at the battery.
0 = +ε – IR2
Solve for I
Write Kirch loop for bottom loop.
Set two expressions for I equal to eliminate I.
Recognize R1, R2 and R1+R2 are proportional to 46, 54 and 100, respectively.
Substitute numbers for Rs and solve for ε

3. IB 5.2 p225 #25
Copy diagram, assign currents, labeled as I1 through top battery to the left, I2, on bottom wire to the right, and I3 middle wire to the rigt.
Write Junction rule I1 = I2 + I3
Write top loop rule counting CCW.
0 = +3 – 20 I3 -30 I3 Solve for I3
Write bottom loop rule counting ccw
0 = – 2 (negative because current over battery backwards) I I I3 (middle wire resistors positive because current over battery in opposite direction of counting)

4. IB 5.2 p225 #25 Substitute for I3 and solve for I2
Use the junction rule to find I1
I2 in Resistor 10, V = I2 (10)
I3 in Resistors 20 and 30
V for 20 = I3 (20)
V for 30 = I3(30)

5. IB 5.2 p225 #26 Copy diagram Assign currents Write Junction rule.
Write Loop rules
Solve algebra

6. IB 5.2 p225 #28 a) Read graph for resistor x at 1.5 V
Read graph for resistor y at 1.5 V
Apply Junction rule to find current through the battery

7. IB 5.2 p225 #28 b)
Use trial and error on the graph to find the current (y axis) where the sum of the (x values) is 1.5 V. Occurs at or just about 1A.

8. IB 5.2 p225 #29 Copy diagram, assign currents.
I1 to left on top wire, I2 to right on A to C and I3 to left on lower wire.
Apply junction rule

9. IB 5.2 p225 #29
Just like #24, I3 = 0 so I1 = I2 and we can drop subscripts
Write top loop rule. Solve for I.
Write bottom loop rule. Value of resistor is proportional to distances, x/1 time 4 (the total distance)
Solve for x