Math Problem Statement

Solve this parallel circut question

Determine the current flowing through R_2, given: R_1 = 3 Ω, R_2 = 5 Ω, and I_1 = 13 A.

Solution

This is a parallel circuit problem, and we're given the following dataThis is a parallel circuit problem, and we're given the following

  • R1=3ΩR_1 = 3 \, \Omega
  • R2=5ΩR_2 = 5 \, \Omega
  • I1=13AI_1 = 13 \, A

The goal is to determine the current flowing through R2R_2.

Step-by-step Solution:

  1. Identify the voltage across the resistors: Since R1R_1 and R2R_2 are in parallel, the voltage across both resistors will be the same, which we can calculate using Ohm's Law:

    V=I1R1V = I_1 \cdot R_1 Where:

    • I1=13AI_1 = 13 \, A
    • R1=3ΩR_1 = 3 \, \Omega

    Substituting values: V=13A3Ω=39VV = 13 \, A \cdot 3 \, \Omega = 39 \, V

  2. Determine the current through R2R_2: Now, using Ohm's Law again for R2R_2, we can calculate the current I2I_2 through R2R_2. The formula is:

    I2=VR2I_2 = \frac{V}{R_2} Substituting the values of V=39VV = 39 \, V and R2=5ΩR_2 = 5 \, \Omega:

    I2=39V5Ω=7.8AI_2 = \frac{39 \, V}{5 \, \Omega} = 7.8 \, A

Final Answer:

The current flowing through R2R_2 is 7.8A\boxed{7.8 \, A}.


Would you like further details on any part of this solution or have additional questions?

Here are 5 related questions:

  1. How would the current change if R2R_2 were doubled?
  2. What would be the total current if both resistances were equal?
  3. How can we calculate the total resistance in this parallel circuit?
  4. What is the relationship between voltage, current, and resistance in parallel circuits?
  5. How do parallel circuits behave compared to series circuits?

Tip:

In parallel circuits, the voltage across each branch is the same, but the current divides according to the resistance of each branch.

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Math Problem Analysis

Mathematical Concepts

Parallel Circuits
Ohm's Law
Current Division

Formulas

Ohm's Law: V = I * R
Current in a parallel resistor: I = V / R

Theorems

Ohm's Law
Parallel Circuit Behavior

Suitable Grade Level

Grades 10-12