Combinations of Resistors Series and Parallel Rules Ohm’s Law Current Divider Rules (CDR) Kirchhoff’s Laws

Series Circuits Each resistor has the SAME Current (I) through it. Each resistor has a DIFFERENT Voltage (V) across it. Series Facts

Resistors in series ADD up.

Parallel Circuits Each resistor has the SAME Voltage (V) across it. Between nodes “a” and “b” there is one voltage. Each resistor has a DIFFERENT Current (I) through it. Parallel Facts

Parallel resistors can be combined (reduced) by adding the reciprocals of resistor vales, then inverting your answer. Parallel Facts

When a circuit “branches” the current divides just like when a river divides, water (current) will flow through each branch. Parallel resistors have different currents, if the resistor values are different. Parallel Facts

Parallel resistors have the SAME voltage across them. But different currents. Current divides (splits). Parallel Facts

Resistors RESIST the flow of current. The smaller the resistor, the larger the current. Since, R 1 I 2

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Georg Simon Ohm (16 March 1789 – 6 July 1854) was a German physicist and mathematician. As a high school teacher, Ohm began his research with the new electrochemical cell, invented by Italian scientist Alessandro Volta. Using equipment of his own creation, Ohm found that there is a direct proportionality between the potential difference (voltage) applied across a conductor and the resultant electric current. This relationship is known as Ohm's law.

Current divides at a node. I3I3 ITIT

Equivalent resistance for the two parallel resistors.

Find TOTAL resistance for the circuit. R EQ = 909  ITIT I TOTAL is the total current leaving the power supply.

Use CDR to find I 3 I3I3 Current divides at a node. ITIT Question: What is the value of the current that goes through R1?

Measuring current and voltage. Current is measured through a resistor Voltage is measured across a resistor Internal resistance in a power supply Ammeters measure current Voltmeters measure Voltage

Everything has resistance. Resistance slows the flow of current. Internal resistance in a power supply Internal resistance & TERMINAL VOLTAGE.  is EMF, it is the rated voltage. EMF means Electromotive Force. What we think we have. What we actually have. Internal resistance lowers the battery voltage.

Internal resistance in a battery or power supply only occurs once current flows. Current only flows when a device (resistor) is connected to a power supply. Internal resistance in a power supply  is EMF. This is the rated voltage. This is the voltage of the battery. 3V is the   for this battery. Internal resistance & TERMINAL VOLTAGE.

Everything has resistance.  is EMF, it is a VOLTAGE. It is NOT a Force. Terminal Voltage is the actual voltage you get out of a battery once it is hooked to a circuit. V AB is the Terminal Voltage. B A Terminal Voltage is the EMF minus the “voltage drop” due to “r”.

Gustav Robert Kirchhoff (12 March 1824 – 17 October 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. Kirchhoff developed TWO laws for solving circuit problems. The sum of the currents entering a node must equal the sum of the currents exiting a node. (Kirchoff's Law #1) The voltages around a closed path in a circuit must sum to zero. (Kirchoff's law #2)

The current entering any junction is equal to the current leaving that junction. i 2 + i 3 = i 1 + i 4

Circuit Equations Circuit Symbols variable resistor lamp