Math Problem Statement

Determine the total resistance in a circuit containing one 8 Ω and one 86 Ω resistor with a total voltage of 202 V.

Solution

The problem asks for the total resistance in a circuit containing two resistors: one with a resistance of 8 Ω and another with a resistance of 86 Ω, with a total voltage of 202 V. Based on the provided circuit, we need to determine whether these resistors are connected in series or in parallel.

Since the resistors are shown side by side with the same current flowing through both, this indicates a series circuit. In a series circuit, the total resistance RtotalR_{\text{total}} is the sum of the individual resistances:

Rtotal=R1+R2R_{\text{total}} = R_1 + R_2

Where:

  • R1=8ΩR_1 = 8 \, \Omega
  • R2=86ΩR_2 = 86 \, \Omega

Now, let's calculate the total resistance:

Rtotal=8Ω+86Ω=94ΩR_{\text{total}} = 8 \, \Omega + 86 \, \Omega = 94 \, \Omega

Therefore, the total resistance is 94.0 Ω.

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Related Questions:

  1. How does the total voltage affect the current in a series circuit?
  2. What is the formula for total resistance in a parallel circuit?
  3. How would the total resistance change if the resistors were in parallel instead of series?
  4. What is the current flowing through the circuit with the given total resistance and voltage?
  5. How can you calculate the voltage drop across each resistor in a series circuit?

Tip:

In a series circuit, the current remains the same across all components, while the voltage divides proportionally to the resistances.

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Math Problem Analysis

Mathematical Concepts

Ohm's Law
Series Circuits

Formulas

R_total = R1 + R2 (for series circuits)

Theorems

Series Resistance Theorem

Suitable Grade Level

Grades 9-12