Introduction
Kirchhoff’s Laws are fundamental principles in electrical engineering that govern how current and voltage behave in electronic circuits. Parallel circuits are one of the most important circuit configurations in electronics, and understanding how Kirchhoff’s Laws apply to them is essential for any electrical engineer or hobbyist. This article will explore the answer key for Kirchhoff’s Laws in parallel circuits.
What Are Kirchhoff’s Laws?
Kirchhoff’s Laws are two fundamental principles that govern how current and voltage behave in electronic circuits. The first law, also known as Kirchhoff’s Current Law (KCL), states that the sum of all currents entering and leaving a node in a circuit must be equal to zero. The second law, also known as Kirchhoff’s Voltage Law (KVL), states that the sum of all voltages around any closed loop in a circuit must be equal to zero.
What Is a Parallel Circuit?
A parallel circuit is a circuit configuration in which the components are arranged in parallel with each other. This means that the components are connected across the same two points in the circuit, and each component has its own branch in the circuit. In a parallel circuit, the voltage across each component is the same, while the current through each component is different.
Applying Kirchhoff’s Laws to Parallel Circuits
To apply Kirchhoff’s Laws to parallel circuits, we must first identify all the nodes and loops in the circuit. Then, we can use KCL to calculate the current at each node, and KVL to calculate the voltage drop across each loop. In a parallel circuit, KCL is used to calculate the total current in the circuit, while KVL is used to calculate the voltage drop across each component.
Example
Let’s consider a simple parallel circuit with two resistors and a voltage source. The voltage source has a voltage of 12V, and the two resistors have resistances of 4Ω and 6Ω, respectively. To apply Kirchhoff’s Laws to this circuit, we first identify the nodes and loops: – Node 1: The point where the voltage source is connected to the circuit. – Node 2: The point where the two resistors are connected to each other. – Loop 1: The top loop that includes the voltage source and the 4Ω resistor. – Loop 2: The bottom loop that includes the voltage source and the 6Ω resistor. Using KCL, we can calculate the current at each node: – Node 1: The current entering the node is equal to the current leaving the node, which is the total current in the circuit. Therefore, the current at node 1 is I = V/R = 12V / (4Ω + 6Ω) = 1.2A. – Node 2: The current entering node 2 is equal to the current leaving node 2, which is the current through the 4Ω resistor. Therefore, the current at node 2 is I = V/R = 12V / 4Ω = 3A. Using KVL, we can calculate the voltage drop across each loop: – Loop 1: The voltage drop across the voltage source is equal to the voltage drop across the 4Ω resistor, since they are in series. Therefore, the voltage drop across the 4Ω resistor is V = IR = 1.2A * 4Ω = 4.8V. – Loop 2: The voltage drop across the voltage source is equal to the voltage drop across the 6Ω resistor, since they are in series. Therefore, the voltage drop across the 6Ω resistor is V = IR = 1.2A * 6Ω = 7.2V.
Conclusion
Kirchhoff’s Laws are essential principles in electrical engineering, and understanding how they apply to parallel circuits is crucial for any engineer or hobbyist. By applying KCL and KVL to parallel circuits, we can calculate the currents and voltages in the circuit, and ensure that the circuit functions properly. With this answer key, you can now confidently apply Kirchhoff’s Laws to parallel circuits and solve any circuit design problem that comes your way.
