Unit 4: Electric Circuits

Concepts

Circuit - A closed loop with a power (voltage) source. Components of a circuit can include:

• Battery - the power source. Pushes charge from one end of the circuit to the other.
• Resistor - used to regulate the flow of current in a circuit to prevent other components from getting too much voltage.
• Capacitor - A device which can be used to store electric charge. The device consists of 2 parallel plates, usually with some kind of insulating material in between called a dielectric. The amount of charge a capacitor can hold tends to be proportional to the potential difference between the plates. The measure of how much charge a capacitor can store is called capacitance.
• Switch - Can be inserted into a circuit to control the flow of current by opening or closing the switch.

Series and parallel - The two ways that resistors can be attached to each other in a circuit. In series connections, resistors are attached one after another in a single path. In parallel connections, resistors are attached in seperate paths.

Resistivity - A measure of how much a specific material resists the flow of charge through it.

Kirchhoff's Laws - A set of rules that define the behavior of circuits. The junction rule states that the sum of any currents that enter a junction must equal the sum of currents that exit a junction. The loop rule states that the sum of voltage gains (a positive change in velocity) and voltage drops (a negative change in velocity) in a circuit must equal zero.

Formulas

V = IR - Ohm's law, used to analyze circuits. Voltage = (current)(resistance).

R = ρl/A - Used to look at the resistivity of a material. Resistance = ((resistivity)(length of resistor))/cross sectional area of the resistor.

P = IV - Used to find the power of a resistor or a device. Power = (current)(voltage).

P = E/t - Used to find the energy a resistor or device uses. Power = energy/time.

R_eq = R₁ + R₂ + R₃ + ... - The formula version of the loop rule, used to find the resistance of series circuits. Resistance of the circuit = resistance of each resistor added up.

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ + ... - The formula version of the junction rule, used to find the resistance of parallel circuits. The inverse of the resistance of the circuit = the inverse of the resistance of each resistor, added up.

Q = CV - Used to find the capacitance of a capacitor. Charge through capacitor = (capacitance)(voltage through capacitor).

C = (1/4πε_o)A/d - Used to find the capacitance of a capacitor. Capacitance = (dielectric constant)(Coulomb's constant)(area of the plates/distance between the plates).

1/C_eq = 1/C₁ + 1/C₂ + 1/C₃ + ... - Used to find the total capacitance in a series connection. The inverse of the capacitance of the circuit = the inverse of the capacitance of each capacitor, added up.

C_eq = C₁ + C₂ + C₃ + ... - Used to find the total capacitance in a parallel connection. Capacitance of the circuit = capacitance of each capacitor added up.