How do you find equivalent resistance in physics?

Equivalent resistance in physics refers to a single resistance that could replace multiple resistors in a circuit without altering the circuit's overall current or voltage. Here's how to calculate it, based on how the resistors are connected:

Resistors in Series

When resistors are connected end-to-end in a single path, they are in series. The equivalent resistance (Req) in a series circuit is simply the sum of all individual resistances.

Formula:

Req = R₁ + R₂ + R₃ + ...

Example:

If you have three resistors with resistances of 10 ohms, 20 ohms, and 30 ohms connected in series, the equivalent resistance would be:

Req = 10 Ω + 20 Ω + 30 Ω = 60 Ω

• The current flowing through each resistor in a series is same.

Resistors in Parallel

When resistors are connected such that they each have their terminals connected to the same two points, they are in parallel. The reciprocal of the equivalent resistance (1/Req) in a parallel circuit is the sum of the reciprocals of all individual resistances.

Formula:

1/Req = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/R_n

Example:

If you have three resistors with resistances of 10 ohms, 20 ohms, and 30 ohms connected in parallel, the equivalent resistance would be calculated as follows:

1/Req = 1/10 + 1/20 + 1/30 = 6/60 + 3/60 + 2/60 = 11/60

To find Req, take the reciprocal:

Req = 60/11 ≈ 5.45 Ω

• The voltage across each resistor in parallel is the same.

Combining Series and Parallel

Often, circuits have a combination of series and parallel resistors. To calculate the equivalent resistance, you will typically:

1. Identify sections of the circuit where resistors are either strictly in series or parallel.
2. Calculate the equivalent resistance for each of these sections.
3. Replace each section with its equivalent resistance.
4. Repeat steps 1-3 until you have reduced the whole circuit to a single equivalent resistance.

Reference Information:

The provided references confirm the formulas for calculating equivalent resistance. Specifically, they list:

• Req=R 1 ​ +R 2 ​ +R 3 ​ +… This is for resistors connected in series, as demonstrated above.
• 1 /Req ​ = 1/R 1 ​ ​ + 1/R 2 ​ ​ + 1/R 3 ​ ​ …+ 1/R n ​ ​ This is for resistors connected in parallel, as shown above.

The reference also includes the specific example Req=R 1 ​ +R 2 ​ +R 3 which is a specific case for the first formula when there are 3 resistors.