Math Problem Statement
In a series circuit with resistances of 8 52, 12 S, and 20 S2, if the circuit is powered by a 40 V supply, what is the current in the circuit and the total power dissipated?
Solution
In a series circuit, the total resistance is the sum of the individual resistances, and the current can be calculated using Ohm's Law. The power dissipated in the circuit can be found using the formula for power.
Step 1: Find the total resistance
The total resistance in a series circuit is the sum of the individual resistances:
Given:
Step 2: Find the current using Ohm's Law
Ohm's Law states that the current is given by:
Where:
- (the supply voltage)
So, the current in the circuit is .
Step 3: Find the total power dissipated
The power dissipated in a circuit can be calculated using the formula:
Where:
Final Answers:
- The current in the circuit is .
- The total power dissipated is .
Would you like more details on any of the steps or have any questions?
Here are 5 related questions you might find interesting:
- How would the current change if the resistance values were doubled?
- What happens to the total power dissipated if the voltage supply is increased to 80V?
- How would the current and power be affected if the resistors were connected in parallel instead of series?
- How do you calculate the voltage drop across each resistor in a series circuit?
- What is the difference between power dissipated and power supplied in a circuit?
Tip: Always check the configuration of the resistors (series or parallel) before applying formulas, as the calculations for total resistance are different in each case.
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Math Problem Analysis
Mathematical Concepts
Ohm's Law
Power Calculation
Series Circuits
Formulas
R_total = R_1 + R_2 + R_3
I = V / R_total
P = V * I
Theorems
Ohm's Law
Suitable Grade Level
Grades 9-11
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