Resistance & Ohm’s Law

12PHYS - Electricity

Finn LeSueur

2019

Mahi Tuatahi / Starter

Homework booklet Electric Fields Question Five: Static Electricity

Previously we have learned about current:

\[\begin{aligned} & current = \frac{charge}{time} \newline & I = \frac{q}{t} \end{aligned}\]

and voltage:

\[\begin{aligned} & voltage = \frac{\text{Electric field strength}}{charge} \newline & V = \frac{E}{q} \end{aligned}\]

Pātai

What is the third variable that we are missing so far?

Resistance

  • Pātai/Question: What carries the charge in a circuit?
  • Whakatika/Answer: Typically, electrons (\(e^{-}\))
  • Pātai: Why are they able to flow in metals?
  • Whakatika/Answer: Because electrons exist in a “sea”, not bound to one atom but able to move around the solid
  • Pātai: What determines how fast the electrons can flow?
  • Whakatika: Resistance is the measure of how much electrons are impeded in a circuit. How much they are slowed down.

Symbol & Units

  • Resistance has symbol R in equations and has the unit Ohms (\(\Omega\), the Greek letter omega).
  • Resistance is determined by the components in the circuit, and is not usually variable
  • Resistance changes when components are added/removed or when a rheostat (variable resistor) is altered
  • Usually voltage is also fixed by the power supply, so usually only the current change

Resistance & Heat

When current moves through a material with resistance the electrons bump into other atoms. This causes energy to be transferred in the form of vibrations (heat)!

  • The higher the resistance, the more heat produced!
  • The higher the current, the more heat produced!

Ohm’s Law

\[\begin{aligned} & V = IR \newline & voltage = current \times resistance \newline \end{aligned}\]
  • Voltage is measured in:
  • Current is measured in:
  • Resistance is measured in:

Pātai

  1. The resistance of a light bulb is \(1.5k\Omega\). Calculate the current through the bulb when it is connected across a \(12V\) power supply.
  2. When \(9V\) is applied to a resistor, \(0.03mA\) of current flows through it. Calculate the resistance of the resistor.
  3. How much voltage is required to produce \(180\mu A\) of current flowing through a \(0.6M\Omega\) resistor?

Whakatika Tahi

The resistance of a light bulb is \(1.5k\Omega\). Calculate the current through the bulb when it is connected across a \(12V\) power supply.

\[\begin{aligned} & V = IR \newline & I = \frac{V}{R} \newline & I = \frac{12}{1500} \newline & I = 0.008A \end{aligned}\]

Whakatika Rua

When \(9V\) is applied to a resistor, \(0.03mA\) of current flows through it. Calculate the resistance of the resistor.

\[\begin{aligned} & V = IR \newline & R = \frac{V}{I} \newline & R = \frac{9}{0.00003} \newline & R = 300000\Omega \end{aligned}\]

Whakatika Toru

How much voltage is required to produce \(180\mu A\) of current flowing through a \(0.6M\Omega\) resistor?

\[\begin{aligned} & V = IR \newline & V = (180 \times 10^{-6}) \times (0.6 \times 10^{6}) \newline & V = 108V \end{aligned}\]