Math Problem Statement
Solution
The image you provided shows a DC circuit with two resistors, and , connected in series. The circuit has a voltage source of . We are tasked with calculating the voltage, current, and power for each resistor.
1. Total Resistance
Since the resistors are in series, the total resistance is the sum of and :
2. Current in the Circuit
Using Ohm's law, the current through the circuit can be found by dividing the total voltage by the total resistance:
3. Voltage Across Each Resistor
The voltage drop across each resistor can be found using Ohm's law ():
-
For :
-
For :
4. Power Dissipated by Each Resistor
The power dissipated by each resistor is given by :
-
For :
-
For :
Summary of Results:
- Voltage across
- Voltage across
- Power dissipated by
- Power dissipated by
Would you like further details on any of these steps or calculations?
Here are five related questions you might explore next:
- What is the total power dissipated in the circuit?
- How would the current change if were doubled?
- How would the voltage across change if the total voltage was reduced to ?
- What would happen to the circuit if was removed (open circuit)?
- How does the power dissipation change if the resistors were arranged in parallel instead of series?
Tip: In a series circuit, the current remains the same through all components, but the voltage divides based on the resistance of each component.
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Math Problem Analysis
Mathematical Concepts
Ohm's Law
Series Circuit Analysis
Power Dissipation
Formulas
R_total = R1 + R2
I = V_total / R_total
V = I * R
P = I^2 * R
Theorems
Ohm's Law
Suitable Grade Level
Grades 9-12
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