Circuitry problem solving
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Intros
Lessons
- Introduction to Circuitry Problem Solving:
- A crash course review on electric circuits.
- Concept 1: How are individual resistances related to voltage drops?
- Concept 2: What can we conclude about resistors in series?
- Concept 3: What can we conclude about resistors in parallel?
- Concept 4: How can we determine the brightness of a lightbulb?
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Examples
Lessons
- Problem Solving for Resistors and Voltage Drops
The two circuits below are configured as shown. Circuit B includes an additional resistor R3 placed in parallel with R1. Compare the values of VR1 and VR2 in circuit B compared to circuit A (no change, decrease, increase)? - Problem Solving for Lightbulb Brightness with Switches
Two identical circuits are shown below, except Circuit A has an open switch and Circuit B has a closed switch. How does each lightbulb (R1,R2,R3,R4 and R5) change in brightness compared to when the switch was open? (same, dimmer, or brighter) - Problem Solving for Complex Circuit with Missing Values
- Solving for Lightbulbs and Terminal Voltage
The circuit is connected to three identical lightbulbs:
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Topic Notes
In this lesson, we will learn:
- A brief review on voltage, current, and resistance
- Establishing 4 main concepts for problem solving:
- Concept #1: a smaller resistor uses up less voltage; a bigger resistor uses up more voltage
- Concept #2: the more resistors added in series with the battery into the circuit will increase the total equivalent resistance
- Concept #3: the more resistors added in parallel with the circuit will decrease the total equivalent resistance
- Concept #4: the brightness of a lightbulb is related to the voltage drop across it (as well as the power dissipated by it)
- Solving questions for more conceptual electric circuits questions:
- Using a combination of all previous concepts and formulas (V,I,R, Ohm’s Law, Vterm, Power)
- As well as applying the 4 main concepts
Notes:
- Before facing problem solving questions for electric circuits that are oftentimes just as conceptual as they are mathematical, one must have a firm understanding of the concepts of each lesson thus far:
- Voltage: staircase analogy, Kirchhoff’s Loop Rule, equal voltage in parallel
- Current: water analogy, Kirchhoff’s Junction Rule
- Resistance: calculating total resistance for series vs. parallel configurations
- Req(series)=R1+R2+R3+...Rn=∑k=1nRk
- Req(parallel)1=R11+R21+R31+...Rn1=∑k=1nRk1
- The conceptual relationships as defined by Ohm’s Law: V=IR
- The shortcut for Ohm’s law; the voltage divider method: Vx=Vtotal⋅RtotalRx
- The concept of terminal voltage and calculations: Vterm=ϵ−Ir
- Power: total power is additive, P=tE and P=IV=I2R=RV2
- Energy: E=Pt and E=IVt
- The 4 main concepts can be summarized as follows:
- I. The greater the resistance of a resistor, the more voltage that it uses up (and vice versa; a smaller resistor uses less voltage)
- II. The more resistors added in series, the greater the equivalent resistance
- III. The more resistors added in parallel, the lesser the equivalent resistance
- IV. The brightness of a lightbulb is related to the voltage it uses up (its voltage drop) as well as, the power dissipated by it
- The brightness of a lightbulb is related to the amount of voltage that it uses up (voltage drop); the more voltage used, the brighter the light bulb
- The voltage drop is dependent on current and resistance (V=IR)
- The brightness of a lightbulb can also be understood as how hot the filament is burning
- The incandescent lightbulb is transforming electrical energy into thermal and light energy; the rate of energy transformation is power
- Power is dependent on voltage (P=IV) as well as current and resistance (P=I2R=RV2 )
- When observing lightbulbs in series:
- Adding more lightbulbs in series will increase the overall resistance, thus diminishing the total current—this leads to a smaller voltage drop across each lightbulb, causing a dimming effect
- Opening a switch or having a single broken lightbulb in the series chain will cause all relevant lightbulbs turn off (the whole circuit will be compromised)
- When observing lightbulbs in parallel:
- Adding more lightbulbs in parallel will decrease the overall resistance, thus increasing the total current—the balance leads to relatively constant brightness across all parallel lightbulbs
- Opening a switch or having a single broken lightbulb will not compromise the whole circuit; only the relevant branch of the circuit will be affected (turned off)
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