Electricity and Circuit Analysis Quiz

Definition: Relationship between voltage (V), current (I), and resistance (R).
Formula: V = I × R
Implications:
- Voltage (V) is measured in volts (V).
- Current (I) is measured in amperes (A).
- Resistance (R) is measured in ohms (Ω).

Types of Circuits:
- Series Circuit: Components connected end-to-end; same current flows through all components.
- Parallel Circuit: Components connected across the same voltage source; voltage remains constant across all components.
Key Principles:
- Kirchhoff's Voltage Law: The sum of the electrical potential differences (voltage) around any closed network is zero.
- Kirchhoff's Current Law: The total current entering a junction equals the total current leaving.

Resistance (R):
- Opposition to current flow.
- Depends on the material, length (L), and cross-sectional area (A) of the conductor.
- Formula: R = ρ × (L/A), where ρ is resistivity.
Resistivity (ρ):
- Material property that quantifies how strongly a given material opposes the flow of electric current.
- Measured in ohm-meters (Ω·m).
- Common values: Copper (1.68 × 10^-8 Ω·m), Aluminum (2.82 × 10^-8 Ω·m).

Series Circuits:
- Total Resistance (R_total) = R1 + R2 + R3 + ...
- Current (I) is the same through all components.
- Voltage (V) splits across components: V_total = V1 + V2 + V3 + ...
Parallel Circuits:
- Total Resistance (R_total) can be calculated using:
  - 1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
- Voltage (V) is the same across all components.
- Current divides among components: I_total = I1 + I2 + I3 + ...

Power (P):
- Rate at which electrical energy is consumed or converted.
- Formula: P = V × I
- Measured in watts (W).
Energy (E):
- Total work done by electrical power over time.
- Formula: E = P × t, where t is time in seconds.
- Measured in joules (J) or kilowatt-hours (kWh).

Example Problems:
1. Ohm's Law: If R = 10 Ω and I = 2 A, find V.
  - V = I × R = 2 A × 10 Ω = 20 V.
2. Series Circuit: R1 = 5 Ω, R2 = 10 Ω; find R_total.
  - R_total = R1 + R2 = 5 Ω + 10 Ω = 15 Ω.
3. Parallel Circuit: R1 = 6 Ω, R2 = 3 Ω; find R_total.
  - 1/R_total = 1/R1 + 1/R2 = 1/6 + 1/3 → R_total = 2 Ω.
4. Power Calculation: If V = 12 V and I = 3 A, find P.
  - P = V × I = 12 V × 3 A = 36 W.
5. Energy Calculation: If P = 60 W and t = 2 hours, find E.
  - E = P × t = 60 W × 7200 s = 432,000 J (or 0.12 kWh).

Defines the relationship between voltage (V), current (I), and resistance (R).
Formula: V = I × R, where V is voltage in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω).

Types of Circuits:
- Series Circuit: Components are connected in sequence, resulting in the same current flowing through each component.
- Parallel Circuit: Components are connected across the same voltage source, maintaining constant voltage while the current can vary.
Key Principles:
- Kirchhoff's Voltage Law states that within a closed loop, the total voltage must equal zero.
- Kirchhoff's Current Law asserts that at any junction, the total current entering equals the total current leaving it.

Resistance (R) is the opposition to current flow, dependent on material type, length (L), and cross-sectional area (A).
Formula: R = ρ × (L/A), where ρ is the resistivity.
Resistivity (ρ) quantifies a material's opposition to electric current flow, measured in ohm-meters (Ω·m).
Common resistivity values include copper (1.68 × 10^-8 Ω·m) and aluminum (2.82 × 10^-8 Ω·m).

Series Circuits:
- Total Resistance: R_total = R1 + R2 + R3 +...
- Current (I) remains constant throughout; voltage (V) divides among components: V_total = V1 + V2 + V3 +...
Parallel Circuits:
- Total Resistance: 1/R_total = 1/R1 + 1/R2 + 1/R3 +...
- Voltage (V) is uniform across all components, while total current divides: I_total = I1 + I2 + I3 +...

Power (P) indicates the rate of electrical energy consumption or conversion.
Formula: P = V × I, with power measured in watts (W).
Energy (E) represents total work done by electrical power over time.
Formula: E = P × t, where t is time in seconds and energy measured in joules (J) or kilowatt-hours (kWh).

Ohm's Law: For R = 10 Ω and I = 2 A, V = 2 A × 10 Ω = 20 V.
Series Circuit: For R1 = 5 Ω and R2 = 10 Ω, R_total = 5 Ω + 10 Ω = 15 Ω.
Parallel Circuit: For R1 = 6 Ω and R2 = 3 Ω, use 1/R_total = 1/6 + 1/3 to find R_total = 2 Ω.
Power Calculation: For V = 12 V and I = 3 A, P = 12 V × 3 A = 36 W.
Energy Calculation: For P = 60 W and t = 2 hours (7200 seconds), E = 60 W × 7200 s = 432,000 J (or 0.12 kWh).