Math Problem Statement

A circuit has three resistors connected in series, with a total current of 1.2 amps. What is the circuit's total voltage? (R1 = 300 Ω, R2 = 90 Ω, R3 = 150 Ω)

Solution

To find the total voltage of the circuit, we can use Ohm's Law:

V=IRtotalV = I \cdot R_{\text{total}}

Where:

  • VV is the voltage across the entire circuit,
  • II is the total current,
  • RtotalR_{\text{total}} is the total resistance in the circuit.

Since the resistors are connected in series, 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=300Ω+90Ω+150Ω=540ΩR_{\text{total}} = 300 \, \Omega + 90 \, \Omega + 150 \, \Omega = 540 \, \Omega

Now, using the total current of 1.2 amps:

V=1.2A×540Ω=648VV = 1.2 \, \text{A} \times 540 \, \Omega = 648 \, \text{V}

Thus, the total voltage across the circuit is 648 volts.

Would you like more details on how this was calculated or have any follow-up questions?

Here are five related questions:

  1. How does the total resistance in a series circuit change if more resistors are added?
  2. What would happen to the total current if the voltage remained the same but the total resistance increased?
  3. How do you calculate voltage drops across individual resistors in a series circuit?
  4. How does Ohm's Law apply in parallel circuits compared to series circuits?
  5. How would the total current change if the resistances of the resistors were reduced by half?

Tip: In a series circuit, the current is the same through all resistors, but the voltage divides according to the resistance values.

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Math Problem Analysis

Mathematical Concepts

Ohm's Law
Series Circuit
Resistor Calculation

Formulas

V = I × R_total
R_total = R1 + R2 + R3

Theorems

Ohm's Law

Suitable Grade Level

Grades 9-12