Direct Current Circuits – Kirchhoff’s Rules & Applications Explained | Chapter 26 of University Physics

Chapter 26 builds on basic circuit concepts to tackle complex DC networks using Kirchhoff’s rules. You’ll learn how to analyze resistor combinations beyond simple series and parallel, see how ammeters and voltmeters are properly connected, explore the transient behavior of RC circuits, and understand real‐world power distribution in homes and vehicles.

Watch the full video summary here for detailed problem‐solving examples.

Resistors in Series & Parallel

Understanding simple combinations is the first step:

• Series: Same current flows through each resistor; R_eq = R₁ + R₂ + …; voltages add.
• Parallel: Same voltage across each branch; 1/R_eq = 1/R₁ + 1/R₂ + …; currents divide inversely by resistance.

Kirchhoff’s Rules for Complex Circuits

When networks can’t be simplified, apply:

• Junction Rule: ∑I_in = ∑I_out (charge conservation).
• Loop Rule: ∑ΔV around any closed loop = 0 (energy conservation).

Careful sign conventions for voltage rises/drops yield linear equations you solve simultaneously for unknown currents and voltages.

Measuring Instruments: Ammeters & Voltmeters

• Ammeter: Inserted in series; very low internal resistance; often uses a shunt resistor to extend range.
• Voltmeter: Connected in parallel; very high internal resistance; uses a series resistor to prevent loading the circuit.
• Potentiometer: Measures emf without drawing current by balancing against a known potential.

R-C Circuits: Transient Behavior

Charging: When connected to a DC source, capacitor charge and current evolve as:

q(t) = Q_f(1 – e^–t/RC), I(t) = (E/R) e^–t/RC,

with time constant τ = R C (≈63% charge after one τ).

Discharging: With the source removed:

q(t) = Q₀ e^–t/RC, I(t) = –(Q₀/RC)e^–t/RC,

so that after one τ, about 37% of the initial charge remains, dissipated as heat in the resistor.

Power Distribution Systems

Real‐world wiring differs by application:

• Household (AC): Parallel connections on hot and neutral lines, protected by breakers or fuses; GFCIs guard against ground faults.
• Automotive (DC): ≈13 V systems using chassis as ground, fused circuits to protect against shorts, which otherwise draw excessive current and heat.

Conclusion

By mastering resistor networks, applying Kirchhoff’s rules, and understanding instrument connection and RC transients, you’ll be able to analyze and design any DC circuit—from bench experiments to vehicle wiring. Practice these techniques to build confidence in complex circuitry.

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