18 Questions
What does Kirchhoff's second law, also known as Kirchhoff's Voltage Law, show?
In any closed loop, the sum of the electromotive forces (EMFs) is equal to the sum of the products of the current and the resistance (potential difference)
In a circuit where the resistances are R1 > R2 > R3, what is true about the current through each resistor?
I1 > I2 > I3
An electrical junction has four wires A, B, C, and D connected to it. Wire A carries 7A going in, wire B carries 5A going out, and wire C carries 2A going in. What does wire D carry?
4A going out
A potential divider contains three resistors of 4 Ω, 7 Ω, and 9 Ω. If the voltage across the 7 Ω resistor is 21 V, what is the supply voltage?
21 V
What is the total resistance (RT) of the circuit shown in the POSTTEST information?
19.33 Ω
What is the value of the current I1 in the circuit shown in the POSTTEST information?
6.21 A
What is the first step in applying Kirchhoff's law to a circuit?
Label the current in each branch with symbols like I1, I2, etc.
In writing a junction equation, how are currents entering and leaving a junction treated?
Currents entering are positive, leaving are negative
When applying the loop rule, what is the sign convention for an electromotive force (EMF)?
Positive if traversed from negative to positive terminal
What is the sign convention for a potential difference across a resistor in a loop equation?
Negative if traversed in the direction of current, positive otherwise
In the sample problem, what are the values of the given EMFs (ε1, ε2, ε3)?
ε1 = 5 V, ε2 = 10 V, ε3 = 12 V
If the resistors in the sample problem have values R1 = 2 Ω, R2 = 3 Ω, and R3 = 4 Ω, which resistor has the highest resistance?
R3
What is the value of the current I1 in the given circuit?
1.19 A
What is the value of the current I2 in the given circuit?
-2.46 A
What is the value of the current I3 in the given circuit?
3.65 A
What is the value of the voltage of the battery on the left in the second circuit?
$10.00 V$
According to Kirchhoff's Current Law, what is the relationship between the currents I1, I2, and I3 at junction A?
I1 - I2 - I3 = 0
What is the value of the current through the $4 \Omega$ resistor in the second circuit?
$3.00 A$
Study Notes
Kirchhoff's Laws
- Kirchhoff's laws are used to analyze electric circuits
- Kirchhoff's Current Law (KCL): the sum of the currents entering a junction is equal to the sum of the currents leaving a junction
- Kirchhoff's Voltage Law (KVL): the sum of the electromotive forces (emf) in a closed loop is equal to the sum of the products of the current and resistance (potential difference) in the loop
Junction Equations
- Junction equation for point A: I1 - I2 - I3 = 0
- Junction equation for point B: -I1 + I2 + I3 = 0
Loop Equations
- Loop equation for loop 1: -ε1 + I1R1 + I2R2 + ε2 = 0
- Loop equation for loop 2: -ε1 - I2R2 - ε3 + I3R3 = 0
- Loop equation for loop 3: -ε1 + I1R1 - ε3 + I3R3 = 0
Solving for Currents
- Substitute junction equations into loop equations to solve for currents
- Example: solving for I1, I2, and I3 in a circuit with given emf and resistance values
Activity 1: Kirchhoff's Law Problem Solving
- Solve for currents in a circuit using Kirchhoff's laws
- Determine the current through each resistor in a given circuit
- Apply Kirchhoff's laws to solve for unknown currents
Activity 2: Circuit Analysis
- Analyze a circuit with given resistances and emf values
- Solve for currents and voltages in the circuit using Kirchhoff's laws
Key Concepts
- Kirchhoff's laws are used to analyze electric circuits
- Junction equations and loop equations are used to solve for currents and voltages in a circuit
- Sign convention for emf and potential difference must be observed when writing loop equations
Test your knowledge on Kirchhoff's Current Law, Kirchhoff's Voltage Law, and circuit analysis concepts. Questions cover the applications and implications of these fundamental electrical laws.
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