Math Problem Statement

What is the equivalent resistance of the given circuit with resistors R1 = 6.8 Ω, R2 = 5.6 Ω, R3 = 9.1 Ω, and R4 = 3.9 Ω?

Solution

The images you've uploaded show an electrical circuit problem that involves calculating the equivalent resistance of a given circuit. The circuit consists of resistors R1R_1, R2R_2, R3R_3, and R4R_4 connected in a combination of series and parallel configurations.

Analyzing the Circuit:

  1. Resistor Configuration:

    • Resistors R2R_2 and R3R_3 are in parallel.
    • The combination of R2R_2 and R3R_3 is in series with R4R_4.
    • This entire combination is then in parallel with R1R_1.
  2. Resistor Values:

    • R1=6.8ΩR_1 = 6.8 \, \Omega
    • R2=5.6ΩR_2 = 5.6 \, \Omega
    • R3=9.1ΩR_3 = 9.1 \, \Omega
    • R4=3.9ΩR_4 = 3.9 \, \Omega

Steps to Find the Equivalent Resistance:

  1. Find the equivalent resistance of R2R_2 and R3R_3 in parallel: 1R23=1R2+1R3\frac{1}{R_{23}} = \frac{1}{R_2} + \frac{1}{R_3} 1R23=15.6Ω+19.1Ω\frac{1}{R_{23}} = \frac{1}{5.6 \, \Omega} + \frac{1}{9.1 \, \Omega} Calculate R23R_{23}.

  2. Add R4R_4 in series with R23R_{23} to get R234R_{234}: R234=R23+R4R_{234} = R_{23} + R_4 Calculate R234R_{234}.

  3. Finally, find the equivalent resistance of R234R_{234} and R1R_1 in parallel: 1Req=1R1+1R234\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_{234}} Calculate ReqR_{eq}.

I'll go ahead and calculate these steps for you.The equivalent resistance ReqR_{eq} of the entire circuit is approximately 3.54Ω3.54 \, \Omega.

Would you like more details on this calculation, or do you have any other questions?

Here are 5 related questions to consider:

  1. How does the equivalent resistance change if R2R_2 and R3R_3 are swapped?
  2. What would be the current flowing through the circuit if the voltage UU is 12V?
  3. How does adding another resistor in series with R4R_4 affect the equivalent resistance?
  4. If R1R_1 is removed, what would be the new equivalent resistance?
  5. How can we simplify a complex circuit with more resistors?

Tip: When resistors are in parallel, the equivalent resistance is always less than the smallest individual resistance in the group.

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Math Problem Analysis

Mathematical Concepts

Ohm's Law
Series and Parallel Circuits
Resistor Combination

Formulas

Parallel Resistance: 1/R_eq = 1/R1 + 1/R2
Series Resistance: R_eq = R1 + R2

Theorems

Ohm's Law
Kirchhoff's Circuit Laws

Suitable Grade Level

Grades 9-12