Ch 28: Fundamentals of Circuits

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 28: Fundamentals of Circuits

Problem 16

Chapter 28, Problem 16

What is the value of resistor R in FIGURE EX28.16?

Verified step by step guidance

Step 1: Recognize that the resistors are connected in series. In a series circuit, the total resistance (R_total) is the sum of the individual resistances: R_total = R1 + R2 + R3.

Step 2: Use Ohm's Law, which states that ΔV = I × R_total, to relate the total voltage (ΔV), current (I), and total resistance (R_total). Rearrange the formula to find R_total: R_total = ΔV / I.

Step 3: Substitute the given values into the formula for R_total. The total voltage is ΔV = 5.0 V, and the current is I = 100 mA = 0.1 A. Calculate R_total using R_total = ΔV / I.

Step 4: Once R_total is calculated, subtract the known resistances (R1 = 10 Ω and R2 = 15 Ω) from R_total to find the unknown resistance R. Use the formula R = R_total - (R1 + R2).

Step 5: Perform the subtraction to isolate the value of R. This will give the resistance of the unknown resistor in the circuit.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. It is mathematically expressed as V = I × R. This fundamental principle is essential for analyzing electrical circuits and determining unknown values such as resistance.

Series Circuit

In a series circuit, components are connected end-to-end, so the same current flows through each component. The total resistance in a series circuit is the sum of the individual resistances. This concept is crucial for understanding how to calculate the total resistance when resistors are connected in series, as seen in the given circuit with a 10 Ω and a 15 Ω resistor.

Total Resistance Calculation

To find the total resistance in a series circuit, you simply add the resistances of all components. In this case, the total resistance (R_total) can be calculated as R_total = R1 + R2 + R, where R1 and R2 are the known resistances (10 Ω and 15 Ω). This total resistance can then be used in conjunction with Ohm's Law to solve for the unknown resistor R.

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