Math Problem Statement
Solution
To find the electromotive force (emf) of the ideal battery in this circuit, we can use Ohm's Law and Kirchhoff's Loop Rule. Let's break it down step by step:
Circuit Configuration:
- The circuit has 6 resistors: , , , , , and .
- The current flows through .
Given Values:
Step 1: Calculate Voltage Drop across
The voltage across is given by Ohm's Law:
Step 2: Simplify the Circuit
- , , and are in series, so their equivalent resistance is:
- , , and are in series, so their equivalent resistance is:
Step 3: Total Resistance of the Circuit
Since the two series combinations are in parallel, the total resistance is: Solving this:
Step 4: Apply Ohm's Law to Find EMF
Using Ohm's Law for the whole circuit, we can calculate the emf () by multiplying the total resistance by the current , which is the same through the entire circuit:
Thus, the emf of the ideal battery is approximately 5.66 V.
Would you like further clarification or details?
Related Questions:
- How does changing affect the total resistance of the circuit?
- What would happen if were removed from the circuit?
- How would the total current change if were doubled?
- What is the significance of the parallel configuration in determining the total resistance?
- Can you calculate the power dissipated in ?
Tip:
When analyzing complex circuits, simplifying series and parallel resistances step by step can help make the analysis much easier!
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Math Problem Analysis
Mathematical Concepts
Ohm's Law
Kirchhoff's Loop Rule
Series and Parallel Circuits
Formulas
Ohm's Law: V = IR
Series Resistance: R_total = R1 + R2 + ...
Parallel Resistance: 1/R_total = 1/R1 + 1/R2 + ...
Theorems
Kirchhoff's Circuit Laws
Suitable Grade Level
Grades 9-12
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