Resistance in a Wire Network?
A wire of resistance R1 is connected in series with another wire of resistance R2. The total resistance of the network is measured to be 6 ohms when a voltmeter is connected across R2. If the voltage applied is 12 volts, find the value of R2.
1 Answer
📌 CONCEPT: In a series circuit, the total resistance is the sum of individual resistances, which is a fundamental principle of current electricity.
📐 RULE / FORMULA: The total resistance (R_total) of a series circuit is given by the formula R_total = R1 + R2, where R1 and R2 are the resistances of the individual wires.
💡 WORKED EXAMPLE: Given R_total = 6 ohms, V = 12 volts, and R1 + R2 = 6 ohms. We can rearrange the formula to find R2: R2 = R_total - R1. However, we lack information about R1. Let's assume R1 = 3 ohms for simplicity. Then, R2 = 6 - 3 = 3 ohms. Alternatively, we can use Ohm's law to find the current I = V/R_total, and then use the formula I = V/R2 to find R2. Using this method, we get R2 = V/I = 12/ (12/6) = 6 ohms.
⚠️ COMMON MISTAKE: Students often confuse the formula for series and parallel circuits, leading to incorrect calculations of total resistance.
10 Jul 26
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