Final answer:
To determine the voltage across and current through elements in a circuit, Ohm's law and Kirchhoff's method are applied. For a circuit with a known voltage source and equivalent resistance, Ohm's law provides the current, and voltage drops across resistors can be determined. The power absorbed by a resistor can also be calculated using the product of its voltage drop and current.
Step-by-step explanation:
Applying Ohm's law and Kirchhoff's method, we can solve for the voltage and current through specific elements in a circuit. For the example provided, we first need a figure of the circuit to apply either mesh analysis or nodal analysis properly. However, we can discuss a general approach based on the information given. If there's a single voltage source of 24V and a calculated equivalent resistance (Req) of 12Ω, we can use Ohm's Law (V = IR) to find the current provided by the voltage source (I = V/Req = 24V/12Ω = 2A). This current is consistent through each resistor if they are in series, or if in parallel, the voltage across each would be the same while the currents would vary inversely with their resistances.
The voltage drop across any resistor can be calculated as Vn = InRn, where In is the current through the resistor and Rn is the resistance. For the 4Ω resistor given as an example, assuming it's in series, the voltage drop would be V = IR = (2A)(4Ω) = 8V. The power absorbed by the same resistor is P = VI = (8V)(2A) = 16W.
Instruments like DC Voltmeters and Ammeters are used to directly measure these values in practical scenarios. Applying Kirchhoff's voltage and current laws would complete the analysis and help understand more complex networks. Kirchhoff's voltage law states that the sum of potential differences around a closed loop is zero, while Kirchhoff's current law states that the sum of currents at a junction is zero (ΣIin = ΣIout).