Final answer:
Element voltages can be expressed as functions of node voltages using nodal analysis and Ohm's law. Ohm's law states that the voltage across a resistor equals the current times the resistance. By applying KCL and KVL, you can determine the power outputs and verify energy conservation within the circuit.
Step-by-step explanation:
Nodal Analysis and Ohm's Law in Electrical Circuits
Expressing element voltages as functions of node voltages is essential in circuit analysis. You start by applying nodal analysis to identify node voltages. After labeling the nodes as a, b, c, and d, you can apply Kirchhoff's Current Law (KCL) to express the node voltages.
With the use of Ohm's Law, which states that the voltage (V) across a resistor equals the product of the current (I) flowing through it and its resistance (R), V = IR, you can link these node voltages to the current through resistors.
For example, to express the voltage across R1 as a function of node voltages, if node a is connected to the positive terminal of the voltage source and node b is on the other side of R1, then the voltage across R1 would be Vab = Va - Vb.
In terms of Kirchhoff's Voltage Law (KVL), for loop abcda, the source voltage (Vs) contributes positively as we go from a to b, while the voltages across resistors subtract as we go from b to c, c to d, and finally, d to a.
Regarding the voltmeter points, for the voltage source (vs), you would connect the voltmeter across the terminals of the source. To measure the potential difference across each resistor, you place the voltmeter across each resistor respectively. For R2 and R3 combined, you would place the voltmeter across the points where the combination starts and ends.
To confirm Ohm's law, you observe that the current through a resistor is proportional to the voltage across the resistor and inversely proportional to its resistance. This is demonstrated by the Ohm's Law simulation, where changes in voltage and resistance impact current accordingly.
Lastly, the conservation of energy in a circuit can be explored by calculating the output power of the voltage source and each resistor. This is done by using the formula Power (P) = V * I, where V is the voltage across the element and I is the current through it. Any discrepancy between the theoretical and measured current through a resistor, as in the lab scenario provided, could be attributed to practical factors such as measurement error or real-world deviations from ideal circuit conditions.