4.5 Kirchhoff’s Junction Rule and the Conservation of Electric Charge

Introduction

Key Vocabulary

• Kirchhoff's junction rule: Also known as Kirchhoff's first law, it states that the total current entering a junction in an electrical circuit must equal the total current leaving the junction.
• Conservation of electric charge: A fundamental law of physics that states that electric charge cannot be created or destroyed, only transferred from one object to another.
• Electrical circuit: A system of electrical components (such as resistors, capacitors, and inductors) connected together to form a closed loop.
• Current: The flow of electric charge through a conductor, measured in amperes (A).
• Voltage: The potential difference between two points in an electrical circuit, measured in volts (V).
• Resistance: The measure of how much a material opposes the flow of electric current, measured in ohms (Ω).
• Ohm's law: A fundamental law of physics that states that the current through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them.
• Capacitance: The ability of a capacitor to store electrical charge, measured in farads (F).
• Inductance: The property of a conductor by which a change in current induces an electromotive force (EMF) in itself and in nearby conductors, measured in henries (H).
• Circuit analysis: The process of studying and analyzing the behavior of electrical circuits using mathematical techniques and principles.

Kirchhoff's Junction Rule

The Conservation of Electric Charge

Application of Kirchhoff's Junction Rule and the Conservation of Electric Charge

Practice Problems

1. In a circuit with three junctions, if the current entering the first junction is 4A, and the current leaving the third junction is 2A, what is the current leaving the second junction?
2. In a circuit consisting of a battery, a resistor, and a capacitor, the charge on the capacitor is 10mC. If the capacitance of the capacitor is 5μF, what is the voltage across the capacitor?
3. In a circuit consisting of a battery, two resistors, and a switch, the switch is closed for 5 seconds, during which time a total charge of 200μC flows through the circuit. If the resistance of one of the resistors is 10Ω and the resistance of the other resistor is 5Ω, what is the voltage across each resistor?

1. By applying Kirchhoff's junction rule, we know that the total current entering the three junctions must equal the total current leaving the three junctions. Therefore, the current leaving the second junction is 4A - 2A = 2A.
2. The formula for the charge on a capacitor is Q = CV, where Q is the charge, C is the capacitance, and V is the voltage. Rearranging this formula gives V = Q/C. Substituting the given values, we get V = 10mC / 5μF = 2V.
3. The total charge that flows through the circuit is equal to the product of the current and the time the switch is closed, which is 200μC / 5s = 40μA. By applying Ohm's law, we can find the voltage across each resistor. The voltage across the 10Ω resistor is V = IR = 40μA * 10Ω = 0.4V. The voltage across the 5Ω resistor is V = IR = 40μA * 5Ω = 0.2V.

Conclusion