8- Resistance And Resistivity

Question 1

Power dissipation

Answer 1

• When charge flows through a resistor, work is done on the resistor due to collisions of charge carriers and the ions of the resistor so power is scattered in the form of internal energy (kinetic energy of the ions, in the form of lattice vibrations)
• as temperature increases these vibrations increase so there are more collisions, and more work is done so more power is lost and resistance has increases
• P = V^2/R or P=I^2×R

Question 2

Circuit types

Answer 2

• in series circuits, resistance adds up over the components in the circuit
• in parallel circuits resistance of the circuit is found by 1/Total resistance = 1/resistance of first branch + 1/resistance of second branch etc
• total resistance is always smaller than the value of the smallest resistor

Question 3

Reistivity formula

Answer 3

-‘rho’ = RA/l
‘rho’ = resistivity is the constant of resistance for a material, what causes the magnitude of resistance
- R = resistance (ohms), A = cross sectional area of resistor (m^2), l = length of resistor (m)
- this causes p.d to decrease in a uniform current-carrying wire as length increases.

Question 4

How to affect resistivity

Answer 4

• increases with higher temperatures as positive metal ions have more Kinetic energy, causing a greater number of collisons
• increases with higher no. Charge carriers
• smaller sized resistor increases resistivity

Question 5

Semiconductors

Answer 5

• thermistors lower resistance with temperature as more de-localised electrons are released with increasing temperature (Negative Temperature Correlation)
• LDR’s use the photoelectric effect to release electrons with illumination and lower resistance
• as n increases with temperature/illumination, I increases due to I=QnAV, so R decreases due to R=V/I
• at high enough temperatures insulators can display this NTC as well as their atomic structure breaks down and electrons are released
• Positive Temperature Correlation can be used as well, and by alloying a semiconductor a 0 Temperature Correlation can be achieved

Question 6

Ohms law

Answer 6

• Resistance = Potential Difference (V) / Current (A)
• Ohms law is a special case of this where pd and current are directly proportional at a constant temperature
• directly proportional means the V/I graph is a straight line through the origin

Question 7

Deriving resistance formula (series circuit)

Answer 7

• Voltage of circuit is total of all component’s voltages, - - Vt = V1 + V2
• V = IR, so IRt = IR1 + IR2
• I is constant in a series circuit so it can be removed, giving Rt = R1 + R2

Question 8

Deriving resistance formula (Parallel circuit)

Answer 8

• Current of parallel circuit is total of each branches current, so It = I1 + I2
• I = V/R, so V/Rt = V/R1 + V/R2
• Voltage is constant across branches so it can be removed, giving 1/Rt = 1/R1 + 1/R2