Math Problem Statement
Solution
To solve this circuit problem, let's analyze the setup and compute the equivalent resistance and the current through the circuit.
Given Data:
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Resistors:
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Potential difference between points and :
Step 1: Determine Equivalent Resistance
The configuration shows and connected in parallel, and their combination in series with .
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Parallel Combination of and : Substituting the values: Calculating this gives:
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Total Equivalent Resistance : Since is in series with , the total resistance is:
Step 2: Calculate the Current in the Circuit
Using Ohm's law:
Step 3: Voltage Across and the Parallel Combination
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Voltage across :
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Voltage across the parallel combination :
Step 4: Current through and
Using the voltage across and :
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Current through :
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Current through :
Summary of Results:
- Total current in the circuit:
- Voltage across :
- Voltage across (parallel part):
- Current through :
- Current through :
Would you like further details on any specific step?
Related Questions:
- How would the total current change if were increased?
- What would happen to the equivalent resistance if and were swapped?
- How is the power dissipated in each resistor calculated?
- How would adding another resistor in series with affect the circuit?
- How does parallel vs. series configuration impact voltage and current distribution?
Tip:
For resistors in parallel, the combined resistance is always less than the smallest resistor in the group, as it provides more paths for current to flow.
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Math Problem Analysis
Mathematical Concepts
Series and Parallel Circuits
Ohm's Law
Electric Circuit Analysis
Formulas
Ohm's Law: V = IR
Parallel Resistance: 1/R_eq = 1/R2 + 1/R3
Series Resistance: R_total = R1 + R_eq
Theorems
Ohm's Law
Parallel and Series Resistor Theorems
Suitable Grade Level
Grades 11-12 or Introductory College Level
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