3 resistors of 3 ohm each connected in series. What is the mean values of resistors?
9 ohm
Understanding Resistors in Series
When resistors are connected in series, they are connected end-to-end along a single path. The same current flows through each resistor in a series connection. The total resistance of the circuit is the sum of the individual resistances.
Calculating Total Resistance in Series
For resistors connected in series, the total resistance ($\small R_{total}$) is calculated by simply adding the resistance values of each resistor.
The formula for total resistance in series is:
$\small R_{total} = R_1 + R_2 + R_3 + ... + R_n$
Where $\small R_1, R_2, R_3, ... R_n$ are the resistance values of the individual resistors.
Applying the Calculation to the Problem
In this problem, we are given:
- Number of resistors: 3
- Resistance of each resistor: 3 ohm ($\Omega$)
- Connection type: Series
Let the resistances be $\small R_1$, $\small R_2$, and $\small R_3$.
- $\small R_1 = 3 \, \Omega$
- $\small R_2 = 3 \, \Omega$
- $\small R_3 = 3 \, \Omega$
Using the formula for total resistance in series:
$\small R_{total} = R_1 + R_2 + R_3$
Substitute the given values:
$\small R_{total} = 3 \, \Omega + 3 \, \Omega + 3 \, \Omega$
$\small R_{total} = 9 \, \Omega$
Thus, the total resistance when three 3 ohm resistors are connected in series is 9 ohm.
Analyzing the Options
Let's look at the given options:
| Option | Value |
|---|---|
| 1 | 18 ohm |
| 2 | 9 ohm |
| 3 | 1 ohm |
| 4 | 6 ohm |
Our calculated total resistance is 9 ohm, which matches Option 2.
While the question asks for the "mean values of resistors", the calculation that yields one of the provided options is the total resistance in series. Therefore, we calculate the total resistance.
Conclusion
The total resistance of three 3 ohm resistors connected in series is 9 ohm. This value is present in the options.
Revision Table: Resistors in Series vs Parallel
| Feature | Series Connection | Parallel Connection |
|---|---|---|
| Diagram | Resistors connected end-to-end in a line. | Resistors connected across the same two points. |
| Current | Same current flows through each resistor. | Current divides among the branches. |
| Voltage | Voltage divides across each resistor. | Same voltage across each resistor. |
| Total Resistance ($\small R_{total}$) | Sum of individual resistances: $\small R_{total} = R_1 + R_2 + ...$ |
Reciprocal of total resistance is sum of reciprocals: $\small \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ...$ |
| Effect on Total Resistance | Total resistance increases. | Total resistance decreases. |
Additional Information on Resistance and Ohm's Law
Resistance ($\small R$): Resistance is a property of a material that opposes the flow of electric current. It is measured in ohms ($\small \Omega$).
Ohm's Law: Ohm's Law describes the relationship between voltage ($\small V$), current ($\small I$), and resistance ($\small R$). It states that the voltage across a resistor is directly proportional to the current flowing through it, provided the temperature remains constant.
The formula for Ohm's Law is:
$\small V = I \times R$
Where:
- $\small V$ is Voltage (measured in Volts, $\small V$)
- $\small I$ is Current (measured in Amperes, $\small A$)
- $\small R$ is Resistance (measured in Ohms, $\small \Omega$)
Understanding series and parallel connections and Ohm's Law is fundamental to analyzing electrical circuits.
Important Questions from Combination of Resistors — Series and Parallel
A cell of negligible resistance and e.m.f 2 volt is connected to series combination of 2 ohm, 3 ohm and 5 ohm. The potential difference across the 3 ohm resistance is:
Ten cells, each of 2 volts emf and 1 ohm internal resistance are connected in series. What is the current flowing through a resistance of 10 ohms connected across this combination of cells?
Three resistor, each equal to 3 Ω are connected so as to form a triangle. The equivalent resistance between any two vertices of the triangle is:
- Two resistors R 1 and R 2 arranged in parallel combination in an electrical closed circuit are made of the same material and of the same thickness. If the length of R 2 is twice the length of R 1, then the total resistance R satisfies
Consider the following part of an electric circuit:
The total electrical resistance in the given part of the electric circuit is
