Key Sections:

• Section 3.1 – Electric Current

• Section 3.2 – Resistance & Power

• Section 3.3 – Compound DC Circuits

• Section 3.4 – Batteries & Meters

• Section 3.5 – Kirchhoff’s Laws

• Section 3.6 – Capacitors in Circuits

Section 3.1: Electric Current

Focus Question: When will charge flow through a conductor?

Definition of Current: Charge moving through a conductor. Impulse flows from high potential to low potential due to potential difference. Conventional current is defined as the direction of positive charge flow; electrons flow in the opposite direction. The flow of charge occurs when there is a complete path for the current and a sufficient potential difference exists to push the charge carriers through the circuit.

Formula: I = ΔQ / Δt Units: Amperes (A)

Examples:

• Example A: Conditions for charging a hollow conducting sphere through a connected wire.

  • Current of 5 mA corresponds to the movement of electrons calculated as approximately 3.1 × 10¹² electrons in one second.

  • Current flows into the sphere; electrons move away.

  • Charge Calculation: Time to obtain a charge of 2 C is found to be 400 seconds.

Section 3.2: Resistance & Power

Focus Question: What affects the rate of current in a circuit?

Resistance:

• Depends on potential difference, length (L), cross-sectional area (A), temperature, and material conductivity.

• Length (L): Longer conductors have higher resistance, which reduces current.

• Cross-Sectional Area (A): Wider conductors allow more current to flow, reducing resistance.

• Temperature: Increased temperature typically raises resistance, thereby affecting current flow.

• Material Conductivity: Conductors with higher conductivity have lower resistance, facilitating greater current.

  Formula: I = ΔV / ρL

• Resistivity (ρ): Property of materials; a perfect conductor has zero resistivity.

Resistor Function: Convert electrical energy to heat, analogous to friction in mechanics.

Ohm's Law: ΔV = I R

Ohmic vs. Nonohmic Circuits:

• Ohmic: Voltage varies linearly with current.

• Nonohmic: Voltage does not vary linearly (e.g., filament lamps).

Power Calculation: P = W / t = Vq

Additional relationships: P = I² R = V² / R

Section 3.3: Compound DC Circuits

Focus Question: How do circuit elements act in series and parallel?

Resistors in Series:

• Same current through both; total voltage is the sum of individual voltages.

  Formula: R_eq = R₁ + R₂

Resistors in Parallel:

• Current splits; same potential across each.

  Formula: 1/R_eq = (1/R₁ + 1/R₂)^-1

Circuit Analysis: Consider current flowing into and out of elements and apply Kirchhoff’s laws to analyze entire circuits.

Section 3.4: Batteries & Meters

Focus Question: How do non-ideal batteries and meters affect the rest of the circuit?

Ammeters: Connect in series with a low resistance to measure current without affecting the circuit. Voltmeters: Connect in parallel with high resistance to measure voltage accurately without drawing current.

Internal Resistance: Real batteries have internal resistance affecting the effective voltage supply. V = ε - I r

Section 3.5: Kirchhoff’s Laws

Focus Question: How are charge and energy conserved in circuits?

Loop Rule: The sum of the voltages around any closed loop is zero.

Node Rule: The current entering any junction equals the current leaving.

Section 3.6: Capacitors in Circuits

Focus Question: How do capacitors behave in a circuit while charging and discharging?

• Charging: Current decreases as the capacitor charges, acts as a short circuit when fully charged.

• In Parallel: Same voltage across each; total charge is the sum of the charge on each.

• In Series: Same charge, voltages add up.

Equations:

• Parallel: C_eq = C₁ + C₂

• Series: 1/C_eq = 1/C₁ + 1/C₂