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Questions and Answers
A wire with a resistance of 10 Ω is connected to a 12 V battery. What is the current flowing through the wire?
A wire with a resistance of 10 Ω is connected to a 12 V battery. What is the current flowing through the wire?
- 120 A
- 100 A
- 0.83 A
- 1.2 A (correct)
A cylindrical wire has a cross-sectional area of 2 mm² and a length of 5 cm. If the wire is made of a material with a resistivity of 1.72 × 10⁻⁸ Ωm, what is its resistance?
A cylindrical wire has a cross-sectional area of 2 mm² and a length of 5 cm. If the wire is made of a material with a resistivity of 1.72 × 10⁻⁸ Ωm, what is its resistance?
- 8.6 × 10⁻⁵ Ω (correct)
- 4.3 × 10⁻⁸ Ω
- 3.44 × 10⁻⁶ Ω
- 1.72 × 10⁻⁸ Ω
Two resistors, R₁ = 5 Ω and R₂ = 10 Ω, are connected in parallel. What is the equivalent resistance of this combination?
Two resistors, R₁ = 5 Ω and R₂ = 10 Ω, are connected in parallel. What is the equivalent resistance of this combination?
- 2.5 Ω
- 3.33 Ω (correct)
- 50 Ω
- 15 Ω
Which of the following statements about Kirchhoff's Current Law (KCL) is true?
Which of the following statements about Kirchhoff's Current Law (KCL) is true?
Two resistors, R₁ = 4 Ω and R₂ = 8 Ω, are connected in series to a 12 V battery. What is the current flowing through the circuit?
Two resistors, R₁ = 4 Ω and R₂ = 8 Ω, are connected in series to a 12 V battery. What is the current flowing through the circuit?
In a circuit with two parallel branches, one with a resistance of 2 Ω and the other with a resistance of 4 Ω, if the total current entering the parallel combination is 6 A, what is the current flowing through the 2 Ω branch?
In a circuit with two parallel branches, one with a resistance of 2 Ω and the other with a resistance of 4 Ω, if the total current entering the parallel combination is 6 A, what is the current flowing through the 2 Ω branch?
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Study Notes
Ohm's Law
- Relates voltage, current, and resistance in a conductor
- Mathematically represented as: V = I × R
- V: voltage (in volts, V)
- I: current (in amperes, A)
- R: resistance (in ohms, Ω)
- States that current flowing through a conductor is directly proportional to the voltage applied and inversely proportional to the resistance of the conductor
Resistivity
- Measure of how much a material opposes the flow of electric current
- Represented by the symbol ρ (rho)
- Unit of measurement is ohm-meters (Ωm)
- Depends on the material, temperature, and other factors
- Formula: R = ρ × L / A
- R: resistance of the material
- L: length of the material
- A: cross-sectional area of the material
Kirchhoff's Laws
- Two laws that describe the behavior of electric circuits
Kirchhoff's Current Law (KCL)
- States that the sum of all currents entering a node in a circuit is equal to the sum of all currents leaving the node
- Mathematically represented as: ΣI_in = ΣI_out
- I_in: currents entering the node
- I_out: currents leaving the node
Kirchhoff's Voltage Law (KVL)
- States that the sum of all voltage changes around any closed loop in a circuit is zero
- Mathematically represented as: ΣV = 0
- V: voltage changes around the loop
Electric Circuits
- Path through which electric current flows
- Composed of components such as resistors, capacitors, inductors, and sources
- Classified into two main types:
- Series circuits: components connected one after the other
- Parallel circuits: components connected between the same two points
- Circuit analysis involves applying Kirchhoff's Laws to determine currents and voltages at various points in the circuit
Current Division
- Method of determining the current through each branch of a parallel circuit
- Formula: I_branch = I_total × (R_total / R_branch)
- I_branch: current through a specific branch
- I_total: total current entering the circuit
- R_total: total resistance of the circuit
- R_branch: resistance of the specific branch
Ohm's Law
- Relates voltage, current, and resistance in a conductor, mathematically represented as V = I × R
- Voltage (V) is measured in volts, current (I) in amperes, and resistance (R) in ohms
- Current flowing through a conductor is directly proportional to the voltage applied and inversely proportional to the resistance of the conductor
Resistivity
- Measures how much a material opposes the flow of electric current, represented by the symbol ρ (rho)
- Unit of measurement is ohm-meters (Ωm), dependent on the material, temperature, and other factors
- Formula to calculate resistance: R = ρ × L / A, where R is resistance, L is length, and A is cross-sectional area
Kirchhoff's Laws
- Describe the behavior of electric circuits, consisting of two laws: Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL)
Kirchhoff's Current Law (KCL)
- States that the sum of all currents entering a node in a circuit is equal to the sum of all currents leaving the node
- Mathematically represented as: ΣI_in = ΣI_out
Kirchhoff's Voltage Law (KVL)
- States that the sum of all voltage changes around any closed loop in a circuit is zero
- Mathematically represented as: ΣV = 0
Electric Circuits
- Defined as a path through which electric current flows
- Composed of components such as resistors, capacitors, inductors, and sources
- Classified into two main types: series circuits and parallel circuits
- Series circuits have components connected one after the other, while parallel circuits have components connected between the same two points
Current Division
- Method of determining the current through each branch of a parallel circuit
- Formula: I_branch = I_total × (R_total / R_branch), where I_branch is the current through a specific branch, I_total is the total current entering the circuit, R_total is the total resistance of the circuit, and R_branch is the resistance of the specific branch
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