ELECTRIC CIRCUITS Students will Solve problems involving current

ELECTRIC CIRCUITS Students will: • Solve problems involving current, charge and time. • Solve problems relating potential difference to energy and charge. • Use Ohm’s Law to relate current, voltage and resistance • Apply Kirchhoff’s Laws to analyze current and voltage in circuits. SPH 3 U/SPH 4 C Findlay

AGENDA 1. 2. 3. 4. 5. 6. Circuit Fundamentals Current Resistance The Battery and Potential Difference Ohm’s Law Kirchhoff’s Laws § Series Circuits § Parallel Circuits

Circuit Fundamentals An electric circuit is a closed loop, with a steady flow of charged particles provided by a source of electrical energy. w A battery converts stored chemical potential energy into electrical energy. w Current electricity is the flow of charged particles along a conductor. w A circuit contains a source of electrical energy, a conductor, and a load. w A load converts electrical energy into light, sound, heat, or motion.

Drawing Circuits Draw a circuit containing three batteries connected to each other, a switch so that electricity can flow through it and three light bulbs connected to each other.

Electric Current Electric current can be compared to the volume flow rate of water. a) b) Volume flow rate of water is a measure of the volume of water flowing past a given point each second. Electric current is a measure of the number of electric charges flowing past a given point each second.

Current • The amount of charge transferred per unit time is referred to as current. w The movement of electrons in a circuit is called electron flow, and is the correct definition of current in a circuit. w Conventional current describes current as positive charges moving from positive to negative poles. Although technically incorrect, conventional current is often used in circuit analysis. w The equation for current is Example A battery delivers a charge of 9. 00 C in 1. 00 min of operation. What amount of current is generated in m. A? The interior of a dry cell or “battery”. Chemicals in the dry cell react to provide electrical energy.

Practice Problems 1. A D-cell battery delivers a charge of 200. 0 C in 65. 0 s. Determine the current produced by this battery. 3. 08 A 2. A car battery provides a current of 600. 0 A for 2. 48 s. Determine the charge provided by the battery. 1. 49 x 103 C 3. A battery has a total charge capacity of 10 800 C. For how long can this battery deliver a current of 450 m. A? 2. 4 x 104 s

DC vs AC Current • Current can have one direction or move back and forth. w Direct current (DC) is a steady current in one direction. w Alternating current (AC) changes direction periodically. Charges in AC move back and forth and do not move from one terminal to another in the circuit. AC is used in household wiring.

Measuring Current Conventional Current § When the direction of DC was first defined, scientists did not know that it was the electrons that pushed each other along the wires. By convention, they agreed that electric current was the flow of positive charges. Electron Flow § The confusing part is that in metal conductors it is the electrons, the negative charges that flow.

Measuring Current The instrument used to measure electric current is called an ammeter. § It must be connected directly in the path of the moving charges. This type of connection is called a series connection.

Resistance • Resistance is the degree to which current is opposed in a circuit. w A resistor is a device that resists or restricts current. w Resistors remove energy from charges and convert it to other forms of energy, such as heat. w Under normal conditions, all components offer some resistance in a circuit, even if resistance is not their primary role. This is a magnetic levitation (maglev) train. It was designed in Germany and has a cruising speed of 500 km/h. Electromagnets provide the magnetic force needed to levitate the train. The electromagnets require large amounts of current to provide adequate magnetic force. Large conducting wires are needed to minimize resistance in the circuits supplying the electromagnets. Superconductors (substances that conduct with zero resistance) may one day provide economical solutions for carrying large amounts of current.

Resistance is an opposition to the flow of charge, resulting in a loss of potential energy. § The magnitude of the electrical resistance of a conductor depends on four variables: § § The The length of the conductor. cross-sectional area of the conductor. material the conductor is made of. temperature of the conductor. The type of material determines how easily it allows electrons to move from one atom to the next. § Conductors allow electrons to move easily; hence, they have very low resistance. § Insulators do not allow electrons to move easily. They have a very high resistance. § Semi-conductors fall somewhere in between.

Colour-Coded Resistors

Example: Colour-Coded Resistance

The Battery and Potential Difference • Batteries increase the potential energy of charges in a circuit. w A battery acts like a pump by increasing the energy of charges, much like a water pump gives water potential energy by pumping it to a higher level. w Electric potential is the electrical potential energy per unit charge, measured in volts (V). It is mathematically expressed as:

Electric Potential Difference w Charges have a greater electric potential before they pass through a load than after. This change in electric potential is potential difference (∆V), which is often referred to as voltage.

Practice Problems 1. A potential difference of 120. 0 V is measured across a light bulb. The light bulb is left on for 30 min allowing a charge of 900 C to flow through it. How much energy is converted to light and heat? 1. 08 x 105 J 2. A charge of 50. 0 C has a change in potential energy of 1. 00 x 10 3 J as it flows through a resistor. What is the potential difference across the resistor? 20. 0 V

Measuring Potential Difference The instrument used to measure electric potential difference is called a voltmeter. § To measure potential rise, the voltmeter must be connected across the source. § To measure potential drop, the voltmeter must be connected across the load. § This type of connection is called a parallel connection.

Ohm’s law • There is a relationship between potential difference, current, and resistance. w German scientist Georg Ohm applied w Ohm’s law can be expressed mathematically. different voltages across a resistor and measured the current. He found a linear relationship between voltage and current. Example A student is asked to determine the value of the resistor in a circuit as shown below. The slope of the line resulting from plotting voltage against current equals resistance. This is the basis of Ohm’s law.

Ohm’s Law

Practice Problems 195. 0 V 2. 25 A 520. 0 V 6. 00 A