Circuit Logic Slides Unit Review
CIRCUIT LOGIC
Mastering Ohm's Law, Kirchhoff's Rules, and the Fundamentals of Electrical Flow
Ohm's Law Essentials
\[ V = I \times R \]
Potential Difference = Current × Resistance
V
Voltage (Volts)
The "push" or pressure that makes charges move.
I
Current (Amperes)
The flow rate of electrical charge.
R
Resistance (Ohms)
The opposition to current flow.
V
I | R
Cover the variable you want to find!
Kirchhoff's Junction Rule
Conservation of Charge
The sum of currents entering a junction must equal the sum of currents leaving the junction.
\[ \sum I_{in} = \sum I_{out} \]
I1 (5A)
I2 (2A)
I3 (?)
Calculation: 5A = 2A + 3A
Kirchhoff's Loop Rule
Conservation of Energy
The algebraic sum of all potential differences (voltages) around any closed loop in a circuit must be zero.
\[ \sum V = 0 \]
Gains from Batteries = Drops across Resistors
12V
V1 = 4V
V2 = 8V
12V − 4V − 8V = 0V
Principle of Superposition
Used to solve circuits with multiple sources. Analyze one source at a time!
1
Deactivate
Turn off all sources except one.
2
Calculate
Find the current/voltage contribution from that single active source.
3
Sum
Add the algebraic contributions from ALL sources to find the total.
Linearity is Key
Only works for linear elements like resistors!
Electric Potential
Potential (V)
Energy per unit charge at a specific point.
\[ V = \frac{W}{q} \]
Potential Difference (ΔV)
The difference in energy between two points. This is what we measure across resistors!
High Potential
Low Potential
Current flows from High to Low potential.
Circuit Logic Review Worksheet Circuit Sparks Review
Topic: DC Circuit Analysis & Fundamentals
Student:
Date:
Part 1: Foundational MCQs
1. A 9 V battery is connected across a 3 Ω resistor in a simple circuit. What is the current through the resistor?
A. 0.33 A
B. 3.0 A
C. 12 A
D. 27 A
2. Which resistor configuration provides the smallest equivalent resistance to a circuit?
A
Two 10 Ω resistors in series
B
Two 10 Ω resistors in parallel
C
Four 10 Ω resistors in series
D
Four 10 Ω resistors in parallel
3. Which of the following changes will cause the current in an electrical circuit to decrease? (Select two answers)
A. Increasing the source voltage
B. Decreasing the source voltage
C. Increasing the circuit resistance
D. Decreasing the circuit resistance
4. If the resistance of a circuit remains constant, which graph best represents the relationship between current (\(I\)) and potential difference (\(V\))?
I
V
Graph A (Linear)
I
V
Graph B (Constant)
I
V
Graph C (Vertical)
I
V
Graph D (Exponential)
5. In a simple series circuit, which physical quantity remains constant at every point along the single path?
A. Electric Potential
B. Current
C. Power
D. Resistance
6. In a parallel circuit containing a 15 V source, what is the potential difference across any single branch?
A. Exactly 15 V
B. Less than 15 V
C. More than 15 V
D. 0 V
7. A 1.5 V battery is connected to a 9 Ω and a 6 Ω resistor in series. Find the total current.
A. 0.1 A
B. 2.1 A
C. 6.0 A
D. 12.5 A
8. A 12 V battery powers two 3 Ω resistors in series. What is the current through each resistor?
A. 2 A
B. 3 A
C. 4 A
D. 6 A
9. Two 10 Ω resistors are connected in parallel to a 9 V battery. What is the total current leaving the battery?
A. 0.45 A
B. 0.90 A
C. 1.80 A
D. 3.60 A
10. A cell phone operates at 3.6 V and dissipates 0.064 W of power. Calculate the current.
A. 0.018 A
B. 0.056 A
C. 1.800 A
D. 5.600 A
Part 2: Structured Problem Solving
Show all formulas and units for full credit.
11. [Ohm's Law] A heating element in an electric kettle draws a current of 12 A when connected to a 240 V supply. Calculate the resistance of the heating element.
12. [Kirchhoff's Junction Rule] At a certain node in a circuit, three wires meet. Wire A carries 4.5 A into the node. Wire B carries 2.1 A out of the node. Determine the magnitude and direction (in or out) of the current in Wire C.
13. [Kirchhoff's Loop Rule] A series loop contains a 20 V battery, a 10 Ω resistor, and an unknown resistor \(R_x\). If the current in the loop is 0.5 A, calculate the voltage drop across \(R_x\).
14. [Superposition Theory] When using the Principle of Superposition to analyze a circuit with multiple sources, how do you "deactivate" a voltage source versus a current source?
Voltage Source:
Current Source:
15. [Electric Potential] Calculate the amount of work done by a battery to move 0.05 C of charge through a potential difference of 12 V.
16. [Circuit Combination] Look at the diagram below. Calculate the total equivalent resistance of the network.
10 Ω
10 Ω
5 Ω
Diagram: Parallel group (10 & 10) in series with 5 Ω
17. [KCL Formulation] Write the junction rule equation for a node where \(I_1\) and \(I_2\) are entering, and \(I_3\), \(I_4\), and \(I_5\) are leaving. Then, solve for \(I_4\) if \(I_1=10A, I_2=2A, I_3=4A, I_5=5A\).
18. [Superposition Problem] A circuit has two voltage sources: \(V_1 = 10V\) and \(V_2 = 5V\). If the current contribution from \(V_1\) alone is \(0.8A\) and the contribution from \(V_2\) alone is \(-0.2A\) (opposite direction), find the total current.
19. [Electric Potential Concept] Explain the physical difference between the absolute electric potential at a point and the potential difference across a component.
20. [Parallel Analysis] A 24 V battery is connected to two branches in parallel. Branch 1 has a 12 Ω resistor. Branch 2 has an 8 Ω resistor. Calculate the current in each branch and the total current provided by the battery.
© 2026 Circuit Mastery Sequence
Review Material CA-7-REV
Circuit Logic Answer Key Answer Key
Circuit Sparks Review Worksheet
Teacher Resource
Part 1: Foundational MCQs
B (3.0 A) \(I = V/R = 9/3\)
A (Exactly 15 V) Parallel loops share source voltage.
D (Four 10 Ω in parallel) \(R_{eq} = 10/4 = 2.5 \Omega\)
A (0.1 A) \(I = 1.5 / (9+6) = 1.5/15\)
B, C Lower V or Higher R decreases current.
A (2 A) \(I = 12 / (3+3) = 12/6\)
A (Linear Graph) Direct proportionality: \(I \propto V\).
C (1.80 A) \(I_1 = 9/10 = 0.9A; I_{tot} = 0.9 \times 2\)
B (Current) Conservation of charge in a single loop.
A (0.018 A) \(I = P/V = 0.064 / 3.6\)
Part 2: Structured Problem Solving
11. Resistance Calculation
\(R = V / I = 240V / 12A = 20 \Omega\)
12. Kirchhoff's Junction Rule
\[ \sum I_{in} = \sum I_{out} \]
\(4.5A = 2.1A + I_C \rightarrow I_C = 2.4 A\) (Directed OUT)
13. Kirchhoff's Loop Rule
\(V_{battery} = V_{10\Omega} + V_{Rx}\)
\(20V = (0.5A \times 10\Omega) + V_{Rx} \rightarrow 20V = 5V + V_{Rx} \rightarrow V_{Rx} = 15 V\)
14. Superposition Theory
Voltage: Replace with a short circuit (wire). Current: Replace with an open circuit (removal).
15. Electric Potential Work
\(W = q \Delta V = 0.05 C \times 12 V = 0.6 J\)
16. Combination Resistance
\(R_{parallel} = 10 \Omega / 2 = 5 \Omega\)
\(R_{total} = R_{parallel} + R_{series} = 5 \Omega + 5 \Omega = 10 \Omega\)
17. KCL Formulation
\(I_1 + I_2 = I_3 + I_4 + I_5 \rightarrow 10 + 2 = 4 + I_4 + 5\)
\(12 = 9 + I_4 \rightarrow I_4 = 3 A\)
18. Superposition Application
\(I_{total} = I_1 + I_2 = 0.8 A + (-0.2 A) = 0.6 A\)
19. Potential Concept
Potential is energy per charge at a point relative to infinity or ground (absolute value). Potential difference is the work done to move charge between two specific points (voltage drop).
20. Branch Currents
\(I_1 = 24V / 12\Omega = 2 A\). \(I_2 = 24V / 8\Omega = 3 A\).
Total Current \(I_T = 2A + 3A = 5 A\).
Circuit Logic Study Guide Essential Reference
Circuit Logic Study Guide
Mastering the fundamentals of DC circuit analysis
Physics
Goal of Circuit Analysis
To determine the current (I) through and potential difference (V) across every component in a network using fundamental physical laws.
01
Ohm's Law
Describes the direct relationship between voltage and current for a linear resistor.
\[ V = I \cdot R \]
V = Volts (V) I = Amperes (A) R = Ohms (Ω)
Directly Proportional: \( I \propto V \)
If you double the voltage, you double the current (for constant R).
Inversely Proportional: \( I \propto 1/R \)
If you double the resistance, you halve the current (for constant V).
V
I | R
The Magic Triangle
02
Kirchhoff's Junction Rule
Law of Conservation of Charge
Electric charge cannot be created or destroyed at a node. Every electron entering a junction must leave it.
\[ \sum I_{in} = \sum I_{out} \]
Visual Logic
10A (In) 6A (Out) 4A (Out)
Sum In (10) = Sum Out (6 + 4)
03
Kirchhoff's Loop Rule
Law of Conservation of Energy
The sum of all energy gains (batteries) must equal the sum of all energy drops (resistors) in any closed loop.
\[ \sum V_{drops} = \sum V_{gains} \text{ or } \sum V_{loop} = 0 \]
1. Define a Loop
Choose any continuous path that returns to its starting point.
2. Track Signage
Moving through a battery (-) to (+) is a GAIN. Moving with current through a resistor is a DROP (-).
3. Solve Equation
Set the total sum to zero and solve for the unknown variable.
04
Principle of Superposition
"In a linear circuit with multiple sources, the total response is the sum of the individual responses from each source acting alone."
The Deactivation Rule:
Voltage Source → 0V
Replace with a Short Circuit (wire).
Current Source → 0A
Replace with an Open Circuit (cut/gap).
05
Electric Potential
Potential (V)
Electrical potential energy per unit charge at a point.
\[ V = \frac{W}{q} = \frac{\text{Energy}}{\text{Charge}} \]
Potential Difference (\(\Delta V\))
Also called "Voltage". The work required to move a charge between two points.
Circuit Logic Study Guide Rev 2 Essential Reference
Circuit Logic Study Guide
Mastering the fundamentals of DC circuit analysis
Physics
Goal of Circuit Analysis
To determine the current (I) through and potential difference (V) across every component in a network using fundamental physical laws.
01
Ohm's Law
Describes the direct relationship between voltage and current for a linear resistor.
\[ V = I \cdot R \]
V = Volts (V) I = Amperes (A) R = Ohms (Ω)
Direct Relationship
\( I \propto V \) (at constant R)
Inverse Relationship
\( I \propto 1/R \) (at constant V)
V
I | R
Magic Triangle
02
Series & Parallel Architectures
Series: Single Path
Current (I) Same Everywhere
\[ I_{total} = I_1 = I_2 \]
Voltage (V) Divides/Adds
\[ V_{total} = V_1 + V_2 \]
Resistance (R) Summation
\[ R_{eq} = R_1 + R_2 \]
Ohm's Rule: Total voltage equals total current times equivalent resistance: \( V_{tot} = I \times R_{eq} \).
Parallel: Multi-Branch
Voltage (V) Same in Branches
\[ V_{total} = V_1 = V_2 \]
Current (I) Divides/Adds
\[ I_{total} = I_1 + I_2 \]
Resistance (R) Inverse Sum
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} \]
Ohm's Rule: Each branch current is branch voltage divided by branch resistance: \( I_n = V_{tot} / R_n \).
03
Kirchhoff's Junction Rule
Conservation of Charge
At any node, the sum of entering currents equals the sum of leaving currents.
\[ \sum I_{in} = \sum I_{out} \]
IN OUT OUT
04
Kirchhoff's Loop Rule
Conservation of Energy
The energy supplied by sources must be completely used by resistors in a closed loop.
\[ \sum V_{loop} = 0 \text{ (or } V_{sources} = V_{drops}) \]
Rule 1: Loop Path
Pick any loop and a clockwise or counter-clockwise direction.
Rule 2: Polarity
Batteries (-) to (+) are GAINS. Traveling WITH current through R is a DROP.
Rule 3: Algebra
Sum all potential differences and set the result to zero.
05
