# DRAW the GRAPH - AP Physics The mathematical relationship is Where k = the gradient of the line The mathematical relationship is C=k C2 = k D P=IR 2 Example: Power / Current graph: Power vs Current for an ohmic resistor: 4000

3500 3000 P [W] 2500 2000 1500 1000 500 0 0 1 2 3 I [A] 4

5 6 7 Power vs Current for an ohmic resistor: 4000 3500 3000 P [W] 2500 2000 1500 1000 500 0 0

5 10 15 20 I2 [A2] 25 30 35 40 y is proportional to x2 A 1

2 3 4 5 6 Sketch A vs B Replace A with A2 3 12 Now plot B versus A2, you should now have a straight line 27 through the origin 48 Find the gradient of this line: 75 Apply y= mx + b analysis to 108 determine the relationship equation B

A2 B 1 3 4 12 9 27 16 48

25 75 36 108 120 100 B 80 60 40 20 0 0

1 2 3 A 4 5 6 7 120 100 80 B

60 40 20 0 0 5 10 15 20 A2 25 30

35 40 y is inversely proportional to x PV =nRT nRT P= V 1 Pa V Sample Problem: V(m3) 3.0 P(Pa) Sketch V vs P 1 Replace V with 1/V

1.5 2 1.0 3 0.75 4 0.6 5 0.5 6

Now plot 1/V versus A If your guess was right you should now have a straight line through the origin Find the gradient of this line Apply y= mx + b analysis to determine the relationship equation PV =nRT nRT P= V 1 Pa V PV =nRT nRT P= V

1 Pa V 3.5 3 P(Pa) 2.5 2 1.5 1 0.5 0 0 1 2

3 4 V(m3) 5 6 7 3.5 3 P(pa) 2.5 2

PV =nRT nRT P= V 1 Pa V 1.5 1 0.5 0 0.1 0.2 0.3 0.4 0.5

0.6 1/V m-3 0.7 0.8 0.9 1 1.1 You could use your graphing calculator Or USE a Spreadsheet