Math Problem Statement

A series circuit with three resistors (R1 = 30 Ω, R2 = 10 Ω, R3 = 60 Ω) has a power output of 900 Watts.  How much current flows through the circuit?

Solution

To determine the current flowing through the circuit, we can use the power formula for electrical circuits:

P=I2RtotalP = I^2 R_{\text{total}}

Where:

  • PP is the power (900 W),
  • II is the current (which we need to find),
  • RtotalR_{\text{total}} is the total resistance of the series circuit.

Step 1: Find the total resistance of the circuit

In a series circuit, the total resistance is the sum of the individual resistances:

Rtotal=R1+R2+R3R_{\text{total}} = R_1 + R_2 + R_3

Substitute the given values:

Rtotal=30Ω+10Ω+60Ω=100ΩR_{\text{total}} = 30 \, \Omega + 10 \, \Omega + 60 \, \Omega = 100 \, \Omega

Step 2: Solve for the current II

Now, rearrange the power formula to solve for II:

I=PRtotalI = \sqrt{\frac{P}{R_{\text{total}}}}

Substitute the known values:

I=900100=9=3AI = \sqrt{\frac{900}{100}} = \sqrt{9} = 3 \, \text{A}

Final Answer:

The current flowing through the circuit is 3 A.

Would you like a more detailed explanation or help with other questions?


Here are some related questions:

  1. How does the power in a circuit change if the resistance is doubled?
  2. What happens to the total resistance in a parallel circuit?
  3. How would the current change if we added a resistor in parallel with R2R_2?
  4. Can you calculate the power output in a parallel circuit with the same resistors?
  5. How does Ohm’s Law relate to the calculation of current in series circuits?

Tip: In series circuits, the total resistance is always greater than the resistance of the largest resistor.

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Math Problem Analysis

Mathematical Concepts

Ohm's Law
Power in Electrical Circuits
Series Circuits
Square Root Calculations

Formulas

P = I^2 * R_total
R_total = R1 + R2 + R3
I = sqrt(P / R_total)

Theorems

Ohm's Law

Suitable Grade Level

Grades 10-12