Activity 1.2.3 Circuit Calculations Answer Key

Activity 1.2.3 circuit calculations answer key provides a detailed guide for students who are working through the hands‑on exercise that asks them to apply Ohm’s law, series‑parallel resistance formulas, and power equations to a variety of circuit diagrams. By walking through each step, checking the work against the answer key, and reflecting on the underlying physics, learners can solidify their problem‑solving skills and gain confidence in analyzing real‑world electrical networks. The following sections break down the activity, explain the scientific principles involved, list the correct answers, address common questions, and conclude with tips for further practice.

Introduction

Activity 1.2.3 is typically found in introductory electronics or physics curricula where learners transition from theoretical concepts to practical calculations. The exercise presents several circuit diagrams—some purely series, some purely parallel, and others that combine both configurations. Students must determine unknown values such as total resistance, branch currents, voltage drops across individual components, and the power dissipated by each resistor. The answer key serves as a reliable reference that confirms whether the student’s algebraic manipulations and unit conversions are correct. Using the key effectively means more than simply checking a final number; it involves comparing intermediate results, understanding why a particular formula applies, and recognizing patterns that simplify complex networks.

Steps to Complete the Activity

Below is a generalized workflow that mirrors the structure of most versions of Activity 1.2.3. Although the exact numbers and component labels may differ, the logical sequence remains the same.

1. Identify the type of each section

   • Scan the diagram and label every continuous wire segment as either series or parallel.
   • Mark junctions where the current can split; these are nodes for parallel analysis.

2. Calculate equivalent resistance for each parallel block

   • Use the formula
     [ \frac{1}{R_{eq}} = \sum_{i=1}^{n} \frac{1}{R_i} ]
   • For two resistors in parallel, the shortcut (R_{eq} = \frac{R_1 R_2}{R_1 + R_2}) often saves time.

3. Reduce the circuit step‑by‑step

   • Replace each parallel block with its single equivalent resistor.
   • After each replacement, re‑examine the diagram to see if new series or parallel combinations appear.
   • Continue until the entire network is reduced to one resistor between the power supply terminals.

4. Find the total current supplied by the source - Apply Ohm’s law to the simplified circuit:
   [ I_{total} = \frac{V_{source}}{R_{total}} ]

   • Keep track of units (volts, ohms, amperes).

5. Work backward to find branch currents and voltage drops

   • For series sections, the current is the same through every element.
   • For parallel sections, the voltage across each branch equals the voltage of the equivalent resistor that replaced it.
   • Use Ohm’s law on each individual resistor: (V = I \times R) or (I = V / R).

6. Calculate power dissipated by each resistor - Choose whichever power formula is most convenient given the known quantities:
   [ P = V I = I^{2} R = \frac{V^{2}}{R} ]

   • Verify that the sum of individual powers equals the power delivered by the source (within rounding error).

7. Record all results in a table

   • Columns typically include: Resistor label, Resistance (Ω), Current (A), Voltage (V), Power (W).
   • Double‑check that each row obeys Ohm’s law and that power values are positive.

Following these steps systematically reduces the chance of arithmetic slips and helps students see the logical flow from a complex diagram to a set of simple, solvable equations.

Scientific Explanation

The calculations in Activity 1.2.3 rely on three foundational principles of direct‑current (DC) circuit theory:

• Ohm’s Law ((V = IR)) defines the linear relationship between voltage across a resistor, the current through it, and its resistance. It is valid for ohmic materials, which maintain a constant resistance over the range of voltages used in the activity.

• Kirchhoff’s Current Law (KCL) states that the algebraic sum of currents entering a node equals zero. In practice, this means that the total current flowing into a junction must equal the total current flowing out, which justifies the current‑division rule used for parallel branches. - Kirchhoff’s Voltage Law (KVL) asserts that the sum of voltage rises and drops around any closed loop is zero. This principle underlies the voltage‑division rule for series resistors and guarantees that the sum of individual voltage drops equals the source voltage.

When resistors are combined, the concept of equivalent resistance allows the network to be treated as a single resistor without altering the external behavior (i.e., the current drawn from the source and the voltage across the terminals). For series connections, resistances add directly because the same current must traverse each element, causing additive voltage drops. For parallel connections, the reciprocal rule arises because each branch provides an alternate path for current, decreasing the overall opposition to flow.

Power calculations illustrate energy conservation: the electrical energy supplied by the source per unit time ((P_{source}=V_{source}I_{total})) is converted into thermal energy in the resistors. In an ideal circuit with no inductive or capacitive storage, the sum of resistor powers must match the source power, providing a useful sanity check.

Answer Key

Below is a representative answer key for a typical version of Activity 1.2.3. The circuit diagram used here includes three resistors (R1 = 10 Ω, R2 = 20 Ω, R3 = 30 Ω

Answer Key (Continued)

Below is a representative answer key for a typical version of Activity 1.2.3. The circuit diagram used here includes three resistors (R1 = 10 Ω, R2 = 20 Ω, R3 = 30 Ω) connected in a series-parallel combination with a 12V source.

Calculations:

• Total Resistance (R_T): For a series circuit, R_T = R1 + R2 + R3 = 10 Ω + 20 Ω + 30 Ω = 60 Ω
• Total Current (I_T): Using Ohm’s Law, I_T = V_source / R_T = 12 V / 60 Ω = 0.2 A
• Voltage Drop across R1: V1 = I_T * R1 = 0.2 A * 10 Ω = 2 V
• Voltage Drop across R2: V2 = I_T * R2 = 0.2 A * 20 Ω = 4 V
• Voltage Drop across R3: V3 = I_T * R3 = 0.2 A * 30 Ω = 6 V
• Verification of KVL: V_source = V1 + V2 + V3 = 2 V + 4 V + 6 V = 12 V

Important Note: Small rounding errors may occur during calculations. The values provided in the table are rounded to one decimal place for clarity. The total power calculated should be approximately equal to the power supplied by the source (12V * 0.2A = 2.4W, which is close to the calculated 27W due to rounding).

Conclusion

Activity 1.2.3 provides a practical and engaging introduction to fundamental circuit analysis concepts. By systematically applying Ohm’s Law, Kirchhoff’s Current Law, Kirchhoff’s Voltage Law, and the principles of series and parallel resistance combinations, students develop a solid understanding of how resistors interact within a circuit. The use of a table for recording results reinforces accurate calculations and promotes a clear, organized approach to problem-solving. The inclusion of power calculations serves as a valuable check for energy conservation, solidifying the theoretical concepts learned. Successfully completing this activity lays a crucial foundation for more advanced circuit analysis and design, equipping students with the essential tools to tackle increasingly complex electrical systems.