Math Problem Statement

Determine the voltage dropped across R3 given: ET = 229 V, R1 = 27 Ω, R2 = 47 Ω, R3 = 26 Ω, and R4 = 30 Ω.

Solution

To solve this, we need to calculate the voltage drop across resistor R3R_3 in the circuit. Let's break down the steps involved in determining the voltage across R3R_3.

Given:

  • Total voltage ET=229VE_T = 229 \, \text{V}
  • Resistor values:
    • R1=27ΩR_1 = 27 \, \Omega
    • R2=47ΩR_2 = 47 \, \Omega
    • R3=26ΩR_3 = 26 \, \Omega
    • R4=30ΩR_4 = 30 \, \Omega

Circuit Configuration:

  • R1R_1 is in series with a parallel combination of R2R_2, R3R_3, and R4R_4.

Step 1: Calculate the equivalent resistance of the parallel combination R2R_2, R3R_3, and R4R_4.

The formula for the total resistance of resistors in parallel is:

1Rparallel=1R2+1R3+1R4\frac{1}{R_{\text{parallel}}} = \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4}

Substituting the values:

1Rparallel=147+126+130\frac{1}{R_{\text{parallel}}} = \frac{1}{47} + \frac{1}{26} + \frac{1}{30}

We will calculate the parallel resistance first.The equivalent resistance of the parallel combination RparallelR_{\text{parallel}} is approximately 10.7Ω10.7 \, \Omega.

Step 2: Calculate the total resistance of the circuit.

Since R1R_1 is in series with the parallel combination, the total resistance RTR_T is the sum of R1R_1 and RparallelR_{\text{parallel}}:

RT=R1+Rparallel=27Ω+10.7ΩR_T = R_1 + R_{\text{parallel}} = 27 \, \Omega + 10.7 \, \Omega

We will now compute RTR_T.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, I can still guide you step-by-step through the calculation process. Would you like to continue manually?

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Math Problem Analysis

Mathematical Concepts

Ohm's Law
Series and Parallel Circuits

Formulas

Ohm's Law: V = I * R
Parallel Resistance Formula: 1/R_total = 1/R2 + 1/R3 + 1/R4
Total Resistance in Series: R_total = R1 + R_parallel

Theorems

Ohm's Law

Suitable Grade Level

Grades 10-12