# Electric Current and Direct-Current Circuits

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Electric Current and Direct-Current Circuits
Pre AP Mrs. Martin

The Electric Battery Converts chemical energy into electrical energy
Made of two dissimilar metals One metal becomes positively charged and the other becomes negatively charged

The Electric Battery

Electric Current Flow of electric charge from one place to another
Formula I = Q/t I = Current (Ampere, A) Q = Charge (C) t = time (s)

Example Problem The disk drive in a portable CD player is connected to a battery that supplies it with a current of 0.22 A. How many electrons pass through the drive in 4.5s?

Direction of Current Flow
When speaking of current we are referring to the direction of positive flow. Sometimes called conventional current

Two types of Current Direct Current (DC) Alternating Current (AC)
Current always flows in one direction Alternating Current (AC) Current is periodically reversed

Batteries and Electromotive Force
The potential between terminals of batteries Called EMF Battery has a little internal resistance Also called terminal voltage

Schematic Diagrams Diagram of a circuit

Electromotive Force Difference in electric potential between the terminals Called emf Electron flow begins instantly, but is very slow

Resistance and Ohm’s Law
Opposition to the flow of electrons Like Friction for electricity Ohm’s Law V = IR V = Potential Difference (V) I = Current (A) R = Resistance (Ω)

Example A potential difference of 24 V is applied to a 150 Ω resistor. How much current flows through the resistor?

Resistivity The quality of that characterizes the resistance of a given material. Represented as ρ The greater the resistivity, the greater the resistance

Resistance Formula Example: R = ρ (L/A)
R = Resistance (Ω) ρ = Resistivity (Ω • m) L = Length of wire (m) A = Cross-sectional area of wire (m2) Example: A current of 1.82 A flows through a copper wire 1.75 m long and 1.10 mm in diameter. Find the potential difference between the ends of the wire. The resistivity of copper is 1.68 x 10-8 Ω•m

Temperature Dependence and Superconductivity
As electrons move, the conductor become hot The hotter the conductor, the more resistivity due to increased Kinetic Energy Superconductor Conducts with little or no resistivity Must be at very low temperatures

Electric Power Rate of change of energy Formula Example P = W/t P = IV
P = Power (W) I = Current (A) V = Potential Difference (V) Example A handheld electric fan operates on a 3.00 V battery. If the power generated by the fan is 2.24 W, what is the current supplied by the battery?

Power dissipated in a resistor
P = V2/R P = Power (W) V = Potential Difference (V) R = Resistance (Ω) Example A battery with an emf of 12 V is connected to a 545 Ω resistor. How much energy is dissipated in the resistor in 65s?

Energy Usage Kilowatt hours are used by electric companies to bill for energy usage. 1kWh = 3.6 x 106 J Example A holiday goose is cooked in the kitchen oven for 4.00 hr. Assume that the stove draws a current of 20.0 A, operates at a voltage of V, and uses electrical energy that costs \$0.048 per kWh. How much does it cost to cook your goose?

Household Circuits A household circuit can become overloaded if too much current flows through the circuit than is considered safe Circuit breakers and fuses are installed They act as switches and break the current when the current becomes too large.

Resistors in Series Equivalent Resistance Series Circuit
Total Resistance for a circuit Series Circuit Resistors connected one after another All resistors have the same current Potential Difference across the resistors must sum to the emf of the battery Req = R1 + R2 + R3 …

Example Problem A circuit consists of three resistors connected in series to a 24.0 V battery. The current in the circuit is A. Given that R1 = Ω and R2 = Ω, find (a) the value of R3 and (b) the potential difference across each resistor.

Resistors in Parallel Parallel Circuit
Connected across the same potential difference. The total current is the sum of all the individual currents Potential difference is the same across each resistor 1/Req = 1/R1 + 1/R2 + 1/R3 …

Example Consider a circuit with three resistors , R1 = Ω, R2 = Ω, and R3 = Ω, connected in parallel with a 24.0 V battery. Find (a) the total current supplied by the battery and (b) the current through each resistor.

Combination Circuits In the circuit shown in the diagram, the emf of the battery is 12.0 V, and all the resistors have a resistance of 200 Ω. Find the current supplied by the battery to this circuit.

Kirchhoff’s Rules The Junction Rule Charge conservation
The current entering any point in a circuit must equal the current leaving that point The algebraic sum of the currents should equal zero + current going into the point, - current going out of the point

The Loop Rule Energy Conservation
The algebraic sum of all potential differences around a closed loop in a circuit is zero. Example Problem

Capacitors in Parallel
Equivalent Capacitance is the sum of all the capacitors. ΣC = C1 + C2 + C3 … Example Two capacitors, one 12.0μF and the other of unknown capacitance are connected in parallel across a battery with an emf of 9.00 V. The total energy stored in the two capacitors is J. What is the value of the capacitance C?

Capacitors in Series Σ1/Ceq = 1/C1 + 1/C2 + 1/C3 … Example
Consider the electrical circuit drawn, consisting of a 12 V battery and three capacitors connected partly in series and partly in parallel. Find (a) the equivalent capacitance of this circuit and (b) the total energy stored in each capacitor.

Ammeter Designed to measure the current in a particular part of a circuit. Must be hooked up in series

Voltmeter Measures the potential difference across two points
Must be in parallel to the circuit.