Ohm's Law and Resistivity Quiz

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?

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?

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?

2.5 Ω

3.33 Ω (correct)

50 Ω

15 Ω

Which of the following statements about Kirchhoff's Current Law (KCL) is true?

The sum of all currents entering a node is equal to the sum of all currents leaving the node. Signup and view all the answers

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?

1 A Signup and view all the answers

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?

4 A Signup and view all the answers

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:
1. Series circuits: components connected one after the other
2. 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