Consider the circuit in Figure 1 with resistors R1 = …

Physics Questions
Short Answer
Step by Step Solution
Physics Questions

Consider the circuit in Figure 1 with resistors R1 = 10 ≈í¬©, R2 = 8.1 ≈í¬©, R3 = 7.7 ≈í¬©, and R4 = 112 ≈í¬©, and a battery with emf E = 15 V. Part A: Calculate the current through each resistor using the rules for series and parallel resistors. Provide your answers with two significant figures, separated by commas. Part B: Calculate the current through each resistor using Kirchhoff’s rules, and express your answers with two significant figures, separated by commas.

Short Answer

The process involves calculating the total resistance of series resistors (R1, R2, R3) by summing their values, then using Ohm’s Law to find the current through these resistors. Next, for the parallel resistor RA, the total resistance of the circuit including R_total and RA is calculated, followed by determining the current through RA using the same principles.

Step-by-Step Solution

Step 1: Calculate Total Resistance for Series Resistors

First, you need to find the total resistance of the series resistors, which are R1, R2, and R3. The formula for this is simply the sum of the individual resistances:

  • R_total = R1 + R2 + R3
  • Substituting values: R_total = 10≈í¬© + 8.1≈í¬© + 7.7≈í¬©
  • This will give you the total resistance for the series section of the circuit.

Step 2: Calculate Current Through Series Resistors

Once you have the total resistance from the previous step, you can now calculate the current flowing through the series resistors using Ohm’s Law. Since the current is the same through all series components, the formula is:

  • I_series = E / R_total
  • Where E is the battery’s emf (15 V).
  • This calculation will give you I_series, the current flowing through R1, R2, and R3.

Step 3: Calculate Current Through Parallel Resistor

Now, for the parallel resistor RA, you need to find the total resistance of the circuit that includes R_total and RA. The formula for this is:

  • (1/R_parallel) = (1/R_total) + (1/RA)
  • After finding R_parallel, apply Ohm’s Law again to find the current through RA:
  • I_parallel = E / R_parallel
  • This will give you the current flowing through the parallel resistor RA.

Related Concepts

Series Resistors

Resistors connected end-to-end in a single path for current flow, where the total resistance is the sum of individual resistances.

Ohm’S Law

A fundamental principle relating voltage (v), current (i), and resistance (r) in an electrical circuit, expressed as v = i * r.

Parallel Resistors

Resistors connected across the same two points, providing multiple pathways for current, where the total resistance can be calculated using the reciprocal of the sum of their individual conductances.

Table Of Contents
  1. Consider the circuit in Figure 1 with resistors R1 = 10 Ω, R2 = 8.1 Ω, R3 = 7.7 Ω, and R4 = 112 Ω, and a battery with emf E = 15 V. Part A: Calculate the current through each resistor using the rules for series and parallel resistors. Provide your answers with two significant figures, separated by commas. Part B: Calculate the current through each resistor using Kirchhoff's rules, and express your answers with two significant figures, separated by commas.

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