2 resistors of 4 ohm each are connected in series. What is their equivalent resistance?
8 ohm
Calculating Equivalent Resistance in a Series Circuit
When resistors are connected in series, they are connected one after another in a single path. The total or equivalent resistance of the circuit is the sum of the individual resistances. This means that the current flowing through each resistor is the same, but the voltage across each resistor can be different (unless the resistances are equal).
Formula for Series Resistance Calculation
The formula for the equivalent resistance ($R_{\text{eq}}$) of resistors connected in series is:
\( R_{\text{eq}} = R_1 + R_2 + R_3 + ... + R_n \)
where \( R_1, R_2, ..., R_n \) are the resistances of the individual resistors.
Step-by-Step Calculation of Equivalent Resistance
In this problem, we have two resistors, each with a resistance of 4 ohm. They are connected in series.
Let \( R_1 = 4 \, \Omega \) and \( R_2 = 4 \, \Omega \).
Using the formula for series resistance:
\( R_{\text{eq}} = R_1 + R_2 \)
Substitute the given values:
\( R_{\text{eq}} = 4 \, \Omega + 4 \, \Omega \)
Add the resistances:
\( R_{\text{eq}} = 8 \, \Omega \)
Therefore, the equivalent resistance of the two 4 ohm resistors connected in series is 8 ohm.
Summary of the Calculation
| Resistor | Resistance Value | Connection Type |
|---|---|---|
| Resistor 1 | 4 ohm | Series |
| Resistor 2 | 4 ohm | Series |
| Equivalent Resistance | \( R_1 + R_2 \) | Series Total |
The total resistance is the sum of the individual resistances in a series connection.
Revision Table: Series and Parallel Resistors
| Connection Type | Equivalent Resistance Formula | Current | Voltage |
|---|---|---|---|
| Series | \( R_{\text{eq}} = R_1 + R_2 + ... + R_n \) | Same through each resistor | Divides across each resistor |
| Parallel | \( \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n} \) | Divides through each branch | Same across each resistor/branch |
Additional Information on Resistor Combinations
Understanding how to calculate equivalent resistance for series and parallel circuits is fundamental in circuit analysis. The way resistors are connected significantly affects the total resistance of the circuit, which in turn affects the total current drawn from the power source and the voltage distribution across components.
- In a series connection, adding more resistors increases the total equivalent resistance. This is because the current has to pass through each resistor sequentially, encountering more opposition.
- In a parallel connection, adding more resistors decreases the total equivalent resistance. This is because adding more branches provides more paths for the current to flow, effectively reducing the overall opposition to current.
- Complex circuits often involve combinations of both series and parallel connections. To find the equivalent resistance of such circuits, you typically break them down into smaller series and parallel segments and calculate the equivalent resistance for each segment, simplifying the circuit step by step.
These principles are essential for designing and analyzing electrical circuits in various applications.
Important Questions from Circuit Elements - Teaching
A lead wire and an iron wire are connected in parallel. Their respective specific resistances are in the ratio 40 ∶ 20. The former carries 80% more current than the latter, and the latter is 45% longer than the former. Determine the ratio of their cross-sectional areas latter to former.
The resistor which is nonlinear in nature is called as:
The resistances in the higher range are mostly made of:
A 100 Ω resistor has a conductance of:
- The color code for a 47 Ω resistor with 1% tolerance would be:
