What is the resultant resistance of 3 Ω and 6 Ω resistances connected in series?
9 Ω
Calculating Resultant Resistance in Series Connection
Understanding how to calculate the total resistance when resistors are connected in series is a fundamental concept in electrical circuits. When resistors are connected end-to-end along a single path, they are said to be in series.
What is a Series Connection?
In a series connection, the current flowing through each resistor is the same. The total voltage across the combination is the sum of the voltages across each individual resistor.
Formula for Resistors in Series
For resistors connected in series, the total or equivalent resistance ($R_{total}$) is simply the sum of the individual resistances. If you have resistors $R_1, R_2, R_3, ..., R_n$ connected in series, the formula is:
\(R_{total} = R_1 + R_2 + R_3 + \dots + R_n\)
Step-by-Step Calculation for 3 Ω and 6 Ω in Series
The question asks for the resultant resistance of two specific resistances: 3 Ω and 6 Ω, connected in series. Let's denote these resistances as $R_1$ and $R_2$.
- Given resistance 1, \(R_1 = 3\ \Omega\)
- Given resistance 2, \(R_2 = 6\ \Omega\)
Using the formula for resistors in series:
\(R_{total} = R_1 + R_2\)
Substitute the given values:
\(R_{total} = 3\ \Omega + 6\ \Omega\)
Perform the addition:
\(R_{total} = 9\ \Omega\)
So, the resultant resistance of 3 Ω and 6 Ω resistances connected in series is 9 Ω.
Comparing with Options
Let's look at the provided options:
- 2 Ω
- 9 Ω
- 16 Ω
- 12 Ω
Our calculated resultant resistance is 9 Ω, which matches one of the options.
Summary of Resultant Resistance Calculation
| Resistor | Resistance Value |
|---|---|
| \(R_1\) | 3 Ω |
| \(R_2\) | 6 Ω |
| Connection Type | Series |
| Resultant Resistance (\(R_{total}\)) | \(R_1 + R_2 = 3\ \Omega + 6\ \Omega = 9\ \Omega\) |
Revision Table: Resistance in Series and Parallel
| Feature | Series Connection | Parallel Connection |
|---|---|---|
| Arrangement | End-to-end, single path for current | Across the same two points, multiple paths for current |
| Current | Same through each resistor | Divides among resistors |
| Voltage | Divides across each resistor | Same across each resistor |
| Total Resistance Formula | \(R_{total} = R_1 + R_2 + \dots + R_n\) | \(\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}\) |
| Effect on Total Resistance | Increases total resistance | Decreases total resistance |
Additional Information on Circuit Analysis
Understanding series and parallel combinations is crucial for analyzing more complex electrical circuits. These simple rules allow us to simplify parts of a circuit into single equivalent resistances, making it easier to calculate total current, voltage drops, and power dissipation using Ohm's Law (\(V = IR\)).
In the case of the 3 Ω and 6 Ω resistors in series, the equivalent 9 Ω resistor would behave identically to the series combination in terms of the total voltage across it and the total current flowing through it when connected to a circuit.
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Select the correct answer using the code given below.
