IB DP Physics: SL复习笔记5.2.2 Resistance & Resistors

Resistance

  • As electrons move through the metal wire of a circuit (or any other component), they transfer some of their electrical potential energy to the positive ions of the metal

9.3.1-Electrons-and-resistance

Free electrons collide with metal ions which resist their flow

  • This energy results in an increase in the kinetic energy of the lattice
  • Which means a higher internal energy of the metal
  • The macroscopic result of this transfer is the heating up of the wire
  • Some metals heat up more than others
    • The higher the heating, the higher the resistance
    • Wires are often made from copper because copper has a low electrical resistance
  • The resistance R of a component is defined as:

The ratio of the potential difference across the component to the current flowing through it

  • It is calculated as follows:

Resistance-Equation

  • Where:
    • V = potential difference in volts (V)
    • I = electric current in amperes (A)
    • R = resistance in ohms (Ω)
  • This means that the higher the resistance of a component, the lower the current flowing through it and vice versa
  • In terms of SI base units: 1 Ω = 1 kg m2 s–3 A–2

Worked Example

A charge of 5.0 C passes through a resistor at a constant rate in 30 s. The potential difference across the resistor is 2.0 V.

Calculate the resistance R of the resistor.

Step 1: Write down the known quantities

    • Charge, Δq = 5.0 C
    • Time, Δt = 30 s
    • Potential difference, V = 2.0 V

Step 2: Write down the equation for the resistance R

Resistance-Equation

Step 3: Calculate the current I from the charge and time

Electric-Current-Equation-IB-Physics

Step 4: Substitute the numbers into the above equation

Resistance-Worked-Example-Current-Calculation

I = 0.17 A

Step 5: Substitute this value of the current into the equation for the resistance given in Step 2

Resistance-Worked-Example-Resistance-Calculation

R = 12 Ω

Resistors in Series & Parallel

Resistors in Series

  • When two or more components are connected in series:

10.1.2.4-Resistors-in-series-diagram

The combined resistance of the components is equal to the sum of individual resistances

10.1.2.4-Resistors-in-series-equation

  • This means as more resistors are added, their combined resistance increases and is, therefore, more than the resistance of the individual components

5-2-2-resistors-in-series_sl-physics-rn

Connecting more resistors in series increases the overall resistance

Worked Example

The combined resistance R in the following series circuit is 60 Ω. What is the resistance value of R2?WE-Resistors-in-series-question-image

A.     100 Ω               B.     30 Ω               C.     20 Ω               D.     40 Ω

Step 1: Write down the known quantities

    • Total resistance, R = 60 Ω
    • Resistance of first resistor, R1 = 30 Ω
    • Resistance of third resistor, R3 = 10 Ω

Step 2: Write down the equation for the combined resistance of resistors in series

R = R1 + R2 + R3

Step 3: Rearrange the above equation to calculate the resistance R2 of the second resistor

R2 = R – R1 – R3

Step 4: Substitute the numbers into the above equation

R2 = (60 – 30 – 10) Ω

R2 = 20 Ω

ANSWER: C

Resistors in Parallel

  • When two or more components are connected in parallel:

10.1.2.6-Resistors-in-parallel-diagram

The reciprocal of the combined resistance is the sum of the reciprocals of the individual resistances

10.1.2.6-Resistors-in-parallel-equation

  • This means as more resistors are added, their combined resistance decreases and is, therefore, less than the resistance of the individual components

5-2-2-resistors-in-parallel_sl-physics-rn

Connecting more resistors in parallel decreases the overall resistance

Worked Example

WE-Resistors-in-parallel-question-image-1

Step 1: Write down the known quantities

    • Resistance of first resistor, R1 = R
    • Resistance of second resistor, R2 = 2R
    • Resistance of third resistor, R3 = R

Step 2: Write down the equation for the reciprocal of the combined resistance (1/RTOT) of resistors in parallel

Resistors-in-Parallel-Worked-Example-Equation-for-1RTOT

Step 3: Substitute the given quantities into the above equation

Resistors-in-Parallel-Worked-Example-Calculation-of-1RTOT

Resistors-in-Parallel-Worked-Example-Second-Calculation-of-1RTOT

Step 4: Take the reciprocal of the second equation above to get the combined resistance RTOT

Resistors-in-Parallel-Worked-Example-Result-for-RTOT

ANSWER: D

Exam Tip

The most common mistake in questions about parallel resistors is to forget to find the reciprocal of RT (i.e. 1/RT) instead of RT. Here is a maths tip to rejig your memory on reciprocals:

  • The reciprocal of a value is 1 / value
  • For example, the reciprocal of a whole number such as 2 equals ½
    • Conversely, the reciprocal of ½ is 2
  • If the number is already a fraction, the numerator and denominator are ‘flipped’ round

10.1.2.6-ReciprocalsThe reciprocal of a number is 1 ÷ number

  • In the case of the resistance R, this becomes 1/R
  • To get the value of R from 1/R, you must calculate 1 ÷ your answer
  • You can also use the reciprocal button on your calculator (labelled either x –1 or 1/x, depending on your calculator)

 

 

 

 

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