Circuitry problem solving  Electric Circuits
Circuitry problem solving
Lessons
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, $V_{term}$, 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
 $R_{eq (series) = R_{1} + R_{2} + R_{3} + ... R_{n} = \sum_{k = 1}^n R_{k}}$
 $\frac{1}{R_{eq (parallel)}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + . . . \frac{1}{R_{n}} = \sum_{k = 1}^n \frac{1}{R_{k}}$
 The conceptual relationships as defined by Ohm’s Law: $V=IR$
 The shortcut for Ohm’s law; the voltage divider method: $V_{x} = V_{total} \cdot \frac{R_{x}}{R_{total}}$
 The concept of terminal voltage and calculations: $V_{term} = \epsilon  Ir$
 Power: total power is additive, $P = \frac{E}{t}$ and $P = IV = I^{2}R = \frac{V^{2}}{R}$
 Energy: $E=P t$ and $E=I V t$
 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 ($P=I V$) as well as current and resistance ($P=I^{2}R= \frac{V^{2}}{R}$ )
 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)

Intro Lesson
Introduction to Circuitry Problem Solving:

3.
Problem Solving for Complex Circuit with Missing Values

4.
Solving for Lightbulbs and Terminal Voltage
The circuit is connected to three identical lightbulbs: