Bell Ringer: Define to the best of your ability the definition of: Current Voltage Resistance Explain the behavior of the current and the voltage in a Series Circuit. Explain the behavior of the current and the voltage in a Parallel Circuit.

Notes 7.4: Parallel Circuits This lesson promises to be ELECTRIFYING!

Learning on Your Own: Active Physics – Chapter 5, Section 3, Page 617 – Series & Parallel - Chapter 5, Section 6, Page 646 – V, I, R in Series & Parallel Physics (Red Book) – Chapter 23, Page 616 – Series & Parallel Circuits AllAboutCircuits.com: AllAboutCircuits – Parallel Circuits AllAboutCircuits – Current Divider AllAboutCircuits – Kirchhoff’s Current Law NOTE: Chapter 7: Section 3, build an electric motor

Lesson Objective: Describe parallel circuits. Understand the wiring of a circuit connected in parallel. Define Kirchhoff’s Circuit Laws Calculate currents, voltage drops, and equivalent resistances in parallel circuits.

Parallel Circuit: Which circuit is connected in series and which is connected in parallel? Try to draw a circuit diagram with each.

Parallel Circuit:

Parallel Circuit - Current: A parallel circuit is defined as one having more than one current path connected to a common voltage source. Unlike in a series circuit, the current in a parallel circuit is subject to change as it branches out. Kirchhoff’s Junction Rule (or Current Law): The sum of the current entering any junction must be equal to the sum of the current leaving that junction.

Parallel Circuit - Current: The algebraic sum of the currents entering and leaving any junction of conductors is equal to zero. 𝐼 𝑎 + 𝐼 𝑏 +⋯+ 𝐼 𝑛 =0 𝐼 𝑇 = 𝐼 1 + 𝐼 2 + 𝐼 3 NOTE: Currents entering the junction are assumed to be positive, and currents leaving the junction are considered negative.

Parallel Circuit - Current: 𝐼 𝑇 = 𝐼 1 + 𝐼 2 +⋯+ 𝐼 𝑛 What we see here is that we have a total current of 7.5 A. We see that the current is split between R1 and R2. We also notice that the small resistor has the most current through it because current wants to take the path of least resistance.

Parallel Circuit – Voltage / Electric Potential Difference: In a parallel circuit, the same voltage is present across all the resistors of a parallel group. NOTE: You can still use the Loop Rule.

Parallel Circuit – Resistance: Resistances connected in parallel can be replaced with an equivalent resistance 𝑅 𝑒𝑞 that has the same potential difference V and the same total current I as the actual resistances. 1 𝑅 𝑒𝑞 = 1 𝑅 1 + 1 𝑅 2 + 1 𝑅 3 NOTE: In parallel circuits the equivalent resistance will always be smaller than the resistance of any branch.

Parallel Circuit – Resistance: 1 𝑅 𝑒𝑞 = 1 𝑅 1 + 1 𝑅 2 + 1 𝑅 3 Caution: People often make a mistake when solving for 𝑅 𝑒𝑞 in a parallel because they forget to take 𝑅 𝑒𝑞 out of the denominator.

Parallel Circuit – Resistance: 1 𝑅 𝑒𝑞 = 1 𝑅 1 + 1 𝑅 2 + 1 𝑅 3 To take 𝑅 𝑒𝑞 out of the denominator, divide 1 by your answer so basically the equation actually looks like this: 𝑅 𝑒𝑞 = 1 1 𝑅 1 + 1 𝑅 2 + 1 𝑅 3

Parallel Circuit – Resistance: NOTE: In a Parallel Circuit, the Equivalent Resistance 𝑅 𝑒𝑞 is less than the smallest resistor in the circuit. For instance, if you have a 5 Ω resistor, a 10 Ω resistor, and a 15 Ω resistor in a parallel circuit, you will find the equivalent resistance to be 2.7 Ω. So we see that the equivalent resistance is smaller than the 5 Ω resistor.

𝑹 𝟏 𝑹 𝟐 Total V=IR I=V/R R=V/I P=IV Parallel Circuit - Table: To help solve and the total voltage, total resistance, total current, total power, and all of the corresponding voltages, currents, resistances, and powers through each resistor then it is a good idea to create a table as below : 𝑹 𝟏 𝑹 𝟐 Total V=IR I=V/R R=V/I P=IV 𝑅 𝑒𝑞 =2 𝑜ℎ𝑚𝑠

Parallel Circuit - Table: 𝑹 𝟏 𝑹 𝟐 Total V=IR I=V/R R=V/I P=IV

Parallel Circuit – Equivalent Resistance Example: Given that 𝑅 1 =3 Ω, 𝑅 2 =6 Ω, and 𝐸 𝑎 =30 𝑉. Find the equivalent resistance. 𝑅 𝑒𝑞 =2 𝑜ℎ𝑚𝑠

(Continue on next Slide) Check-Point I: State the rule for current in a parallel circuit. State the behavior of voltage in a parallel circuit. State the behavior of a resistor in a parallel circuit. (Continue on next Slide) 1) Directly 2) The Power will increase. 3) 0.6 C 4) 24 W

Sample Problem: In the parallel circuit below, we have a battery voltage of 𝜀=30 𝑉, a 𝑅 1 =40 Ω, 𝑅 2 =30 Ω, and 𝑅 3 =40 Ω. Solve the Voltage-Current-Resistance-Power Table.

Circuit Terminology – Open Circuits (in Parallel): When comparing the effects of an open in series and parallel circuits, the major difference to be noted is that an open in a parallel circuit would not necessarily disable the entire circuit i.e. the current flow would not be reduced to zero, unless the open condition existed at some point electrically common to all other parts of the circuit.

Circuit Terminology – Short Circuits (in Parallel): A short circuit in a parallel network has an effect similar to a short in a series circuit. In general, the short will cause an increase in current and the possibility of component damage regardless of the type of circuit involved. NOTE: Opens and shorts, alike, if occurring in a branch circuit of a parallel network, will result in an overall change in the equivalent resistance.

Exit Ticket (Higher Order Questions): Two identical resistors connected in series have an equivalent resistance of 4 ohms. The same two resistors connected in parallel will have what equivalent resistance? Compare and contrast voltage and current in series and parallel circuits Three identical light bulbs are wired in series while a matching set are wired in parallel. Both are connected to a constant voltage source. Compare the brightness of the bulbs in the two circuits, and what happens when one bulb burns out.