Equivalent Resistance Series and Parallel Circuits

Two Kinds of circuits

Circuit Diagrams When drawing pictures of circuits, symbols are used as shorthand instead of pictures of components.

Circuit Diagrams Instead of a battery, the symbol is used. (Note: sometimes voltage is called emf or potential difference)

Circuit Diagrams Instead of a resistor, the symbol is used.

Circuit Diagrams Resistors and batteries will be labeled with their respective values most of the time. 9V 10 Ω

Practice Draw a series circuit with a 5V battery and two resistors (one 3Ω and the other 5Ω)

Practice Draw a series circuit with a 5V battery and two resistors (one 3Ω and the other 5Ω) 5V 3 Ω 5 Ω

Practice Draw a parallel circuit with a 12V battery and two resistors (one 6Ω and the other 2Ω)

Practice Draw a parallel circuit with a 12V battery and two resistors (one 6Ω and the other 2Ω) 12V 6 Ω2 Ω

Using Ohm’s Law (V=IR) Ohm’s Law can be applied to A) the WHOLE circuit or B) each RESISTOR separately

Ohm’s Law- WHOLE Circuit What is R total for the circuit? What is the current? 5V 3 Ω 5 Ω

Ohm’s Law- WHOLE Circuit R total : I: 5V 3 Ω 5 Ω

Ohm’s Law- EACH Resistor What is the voltage in each resistor? 5V 3 Ω 5 Ω

Ohm’s Law- EACH Resistor What do we know about the current in each resistor? 5V 3 Ω 5 Ω

Ohm’s Law- EACH Resistor What do we know about the current in each resistor? 5V 3 Ω 5 Ω

Ohm’s Law- EACH Resistor With that in mind we can solve for voltage. 3Ω resistor5Ωresistor 5V 3 Ω 5 Ω

Ohm’s Law- EACH Resistor With that in mind we can solve for voltage. 3Ω resistor5Ωresistor 5V 3 Ω 5 Ω

Ohm’s Law- EACH Resistor With that in mind we can solve for voltage. 3Ω resistor5Ωresistor 5V 3 Ω 5 Ω

Ohm’s Law- EACH Resistor Double check your answer to be sure. 3Ω resistor5Ωresistor 5V 3 Ω 5 Ω

Summary- SERIES Circuits We can write the ways we used Ohm’s Law as: WholeResistor 1, Resistor 2, Resistor3, … Circuit

Practice Pg. 650 Practice A

Ohm’s Law for PARALLEL circuits

PARALLEL (WHOLE circuit) To apply Ohm’s Law (V=IR) to the WHOLE circuit: V=10V 10V 2 Ω4 Ω

PARALLEL (WHOLE circuit) To apply Ohm’s Law (V=IR) to the WHOLE circuit: V=10V 10V 2 Ω4 Ω

PARALLEL (WHOLE circuit) To apply Ohm’s Law (V=IR) to the WHOLE circuit: V=10VR total =1.33ΩI=? 10V 2 Ω4 Ω

PARALLEL (WHOLE circuit) To apply Ohm’s Law (V=IR) to the WHOLE circuit: V=10VR total =1.33ΩI=? V=IR → 10V=I(1.33Ω) 10V 2 Ω4 Ω

PARALLEL (WHOLE circuit) To apply Ohm’s Law (V=IR) to the WHOLE circuit: V=10VR total =1.33ΩI=7.51A 10V 2 Ω4 Ω

PARALLEL (EACH resistor) Now find the CURRENT in each resistor. 10V 2 Ω4 Ω

PARALLEL (EACH resistor) What do we know about VOLTAGE in a PARALLEL circuit? 10V 2 Ω4 Ω

PARALLEL (EACH resistor) The VOLTAGE is the same everywhere… 10V 2 Ω4 Ω V= 10Volts everywhere…

PARALLEL (EACH resistor) Now use V=IR to solve for current at each resistor: 2Ω resistor4Ω resistor 10V 2 Ω4 Ω V= 10V

PARALLEL (EACH resistor) Total Circuit: V=10VR total =1.33ΩI=7.51A Compare the currents 2Ω resistor4Ω resistor 10V 2 Ω4 Ω V= 10V Equal +

Summary of Ohm’s Law For PARALLEL circuits: V total =V 1 =V 2 =V 3 =… I total =I 1 +I 2 +I 3 +… 10V 2 Ω4 Ω

Practice Find A) total resistance in circuit B) current in each resistor 12V 6 Ω2 Ω