Current, voltage, and resistance

George Meshveliani

Lesson Plan

  • What is Electric Current?
  • Understanding Voltage and Resistance.
  • Ohm's Law: The fundamental relationship.
  • Series and Parallel circuits.
  • Analyzing V-I graphs.
  • Practice Problems.
  • Interactive Quiz.

What is Electric Current?

Electric current ($I$) is the rate of flow of electric charge. Think of it as the volume of water flowing through a pipe per second.

Formula: $I = \frac{\Delta Q}{\Delta t}$

Unit: Ampere (A), where $1 \, \text{A} = 1 \, \text{C}/\text{s}$.

What is Voltage?

Voltage ($V$), or potential difference, is the energy per unit charge. It's the "push" that makes current flow, like the pressure difference in a water pipe.

Push

Formula: $V = \frac{\Delta E}{\Delta Q}$

Unit: Volt (V), where $1 \, \text{V} = 1 \, \text{J}/\text{C}$.

What is Resistance?

Resistance ($R$) is the opposition to the flow of electric current. In a water pipe, a narrower section offers more resistance to the water flow.

Formula: $R = \rho \frac{L}{A}$

Unit: Ohm ($\Omega$).

Ohm's Law

Ohm's Law describes the relationship between voltage, current, and resistance in a circuit.

$$V = IR$$

This can be rearranged to solve for any variable:

  • Current: $I = V/R$
  • Resistance: $R = V/I$

Series Circuits

Components are connected one after another, forming a single path for current to flow.

R1
  • Current is the same: $I_{total} = I_1 = I_2 = \dots$
  • Voltage divides: $V_{total} = V_1 + V_2 + \dots$
  • Total Resistance: $R_{total} = R_1 + R_2 + \dots$

Parallel Circuits

Components are connected across the same two points, creating multiple paths for current.

R1
  • Voltage is the same: $V_{total} = V_1 = V_2 = \dots$
  • Current divides: $I_{total} = I_1 + I_2 + \dots$
  • Total Resistance: $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$

Analyzing V-I Graphs

The slope of a V-I graph represents the resistance of the component. A steeper slope means higher resistance.

Practice Problem 1 (Series)

A series circuit has a $12 \, \text{V}$ battery and two resistors with values of $4 \, \Omega$ and $2 \, \Omega$. Calculate the total resistance of the circuit and the current flowing through it.

Hint: Remember to add resistances in series, then use Ohm's Law.

Solution to Problem 1

First, find the total resistance ($R_{total}$):

$$R_{total} = R_1 + R_2 = 4 + 2 = 6 \, \Omega$$

Now, use Ohm's Law to find the total current ($I_{total}$):

$$I_{total} = \frac{V_{total}}{R_{total}} = \frac{12 \, \text{V}}{6 \, \Omega} = 2 \, \text{A}$$

Practice Problem 2 (Parallel)

A parallel circuit has a $12 \, \text{V}$ battery and two resistors with values of $3 \, \Omega$ and $6 \, \Omega$. Calculate the total resistance of the circuit and the total current flowing through the circuit.

Hint: Use the reciprocal formula for parallel resistance, then use Ohm's Law.

Solution to Problem 2

First, find the total resistance ($R_{total}$):

$$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$$

$$R_{total} = 2 \, \Omega$$

Now, use Ohm's Law to find the total current ($I_{total}$):

$$I_{total} = \frac{V_{total}}{R_{total}} = \frac{12 \, \text{V}}{2 \, \Omega} = 6 \, \text{A}$$

Intermediate Problem (Combination Circuit)

A circuit has a $20 \, \text{V}$ battery. The circuit contains a $5 \, \Omega$ resistor in series with a parallel combination of two $10 \, \Omega$ resistors. Find the total resistance and the total current flowing from the battery.

Hint: Simplify the parallel part of the circuit first, then add the series resistance.

Solution to Intermediate Problem

First, find the equivalent resistance of the two parallel resistors ($R_p$):

$$\frac{1}{R_{p}} = \frac{1}{10} + \frac{1}{10} = \frac{2}{10} = \frac{1}{5}$$

$$R_p = 5 \, \Omega$$

Now, add this parallel resistance to the series resistor to find the total resistance ($R_{total}$):

$$R_{total} = R_{series} + R_p = 5 + 5 = 10 \, \Omega$$

Finally, use Ohm's Law to find the total current ($I_{total}$):

$$I_{total} = \frac{V_{total}}{R_{total}} = \frac{20 \, \text{V}}{10 \, \Omega} = 2 \, \text{A}$$

Interactive Quiz

Summary

  • Current ($I$) is the flow of charge.
  • Voltage ($V$) is the push or potential difference.
  • Resistance ($R$) is the opposition to flow.
  • Ohm's Law: $V = IR$.
  • Series circuits have one path, so current is constant.
  • Parallel circuits have multiple paths, so voltage is constant.

Thank You

Any questions?