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

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.