need help w/ physics, current , resistance, potential?

Question

i have a recitation tomorrow and i want to make sure I know what i am doing

http://class.phys.psu.edu/212Recitations/07_Circuits/DC_Circuits.pdf

ok in exercise 1, i figured the order should be B,A,C,D

i dont know if i'm right, but wouldn't less resistance mean more power? so less resistors equal more power? and parallel resistors would yield more power than resistors in a series?


part b of exercise 1


would the order be the same as well?

part2
I have no idea, i need help on this one.

Answer 1

Exercise 1:

The circuit with the highest resistance will draw the least power. The resistance of each circuit is

A: 2*R
B: R/2
C: R/3
D: R+R/2 = 1.5*R

From this, the highest resistance is A, next is D, then B and finally C. That is the order of increasing power.

part b:

The power in each bulb is V^2/R, where V is the voltage across the bulb. Thus, in A, the voltage across each bulb is E/2, so the power in A is

A: E^2/4R

In B and C, the voltage across each bulb is E, so the power is

B,C: E^2/R

Finally, in D, the voltage divides as the resistance ratio; the voltage across the parallel bulbs is

E*(R/2)/(R/2 + R) = E*R/(R+2R) = E/3. Therefore the power in each parallel bulb is

E^2/9R

The voltage across in the series bulb is (2/3)E, so its power is

4E^2/9R

The dimmest bulbs are the parallel bulbs in E (one of these is the"x" bulb); next are the bulbs in A, the next in the series bulb in D, and the brightest in B and C.

Exercise 2:

As instructed in the problem, set up two loop currents, I1 in the left circuit passing through 9V, 20ohms, 9V and another 20ohm. I2 in the other circuit. The middle arm of the circuit will carry both currents, I1 and I2, in opposite directions. See this diagram: http://img509.imageshack.us/img509/7913/circuitsz5.jpg

Sum the voltages in both loops; they must sum to zero:

Loop 1: 9v + I1*20ohm + 9v +(I1 - I2)*20ohm = 0

Loop2 I2*10ohm + 9v + 9v + (I2 - I1)*20ohm = 0

You have two equations in two unknowns (I1 and I2). Multiply out the parentheses and collect terms in I1 and I2 to get equations in the form of

a*I1 + b*I2 = 0
c*I1 +d*I2 = 0

This is your system of equations.