Math Problem Statement
Solution
The problem asks to determine the total resistance between points and in the given circuit. The circuit appears to be a combination of resistors in series and parallel. Here's how we can analyze it step by step:
Step-by-Step Solution:
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Identify Parallel and Series Combinations:
- From the image, we see that the resistors are grouped into parallel and series.
- The resistors , , and are in parallel.
- The resistors , , and are also in parallel.
- These two parallel combinations are then connected in series.
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Calculate Equivalent Resistance for the First Parallel Group (12Ω, 26Ω, 40Ω): The formula for resistors in parallel is: Substituting the values: Solving this gives .
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Calculate Equivalent Resistance for the Second Parallel Group (60Ω, 30Ω, 14Ω): Using the same formula for parallel resistors: Solving this gives .
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Add the Two Equivalent Resistances in Series: Once we have and , we can add them since they are in series:
I will now calculate these values for you.The calculations yield the following results:
- The equivalent resistance of the first parallel group (12Ω, 26Ω, 40Ω) is approximately .
- The equivalent resistance of the second parallel group (60Ω, 30Ω, 14Ω) is approximately .
- Therefore, the total resistance between points and is the sum of these two, which is approximately .
Let me know if you want any more details or explanations.
Here are some related questions to explore further:
- What is the formula for calculating resistance in parallel and series circuits?
- How does changing one resistor in a parallel circuit affect the overall resistance?
- What are the practical applications of parallel and series resistances in real-world circuits?
- How would adding an additional resistor in series to the current setup change the total resistance?
- How can we verify the total resistance in a real circuit using multimeters?
Tip: Always double-check whether resistors are in series or parallel before applying formulas to ensure correct calculations.
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Math Problem Analysis
Mathematical Concepts
Electrical Circuit Analysis
Series and Parallel Resistors
Ohm's Law
Formulas
1 / Req = 1 / R1 + 1 / R2 + ... + 1 / Rn (for parallel resistors)
Req = R1 + R2 + ... + Rn (for series resistors)
Theorems
Series and Parallel Resistance Theorem
Suitable Grade Level
College Level or Advanced High School (Physics, Electrical Engineering)
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