Math Problem Statement

count the electricity A and resistance R2

Calculate the current in the circuit and the resistance of resistor R2.

Solution

The problem involves finding the current (II) in the circuit and the resistance R2R_2. Here's how we can solve it using the provided information:

Given Data:

  • Voltage source Vtotal=6.0VV_{\text{total}} = 6.0 \, \text{V}
  • Resistor R1=22ΩR_1 = 22 \, \Omega
  • Voltage across R2R_2, VR2=2.4VV_{R_2} = 2.4 \, \text{V}

Step 1: Calculate the total current (II) in the circuit.

The resistors R1R_1 and R2R_2 are connected in series because the same current flows through both. The voltage drop across R1R_1 is calculated using Kirchhoff's Voltage Law (KVL), where the sum of voltage drops across resistors equals the total supplied voltage.

The total voltage is: Vtotal=VR1+VR2V_{\text{total}} = V_{R_1} + V_{R_2} Thus, the voltage across R1R_1 is: VR1=VtotalVR2=6.0V2.4V=3.6VV_{R_1} = V_{\text{total}} - V_{R_2} = 6.0 \, \text{V} - 2.4 \, \text{V} = 3.6 \, \text{V}

Step 2: Use Ohm's Law to find the current.

Now, using Ohm's Law V=IRV = IR, we can calculate the current in the circuit. The current II is the same through both resistors in a series circuit, so we use R1R_1 and VR1V_{R_1}:

I=VR1R1=3.6V22Ω=0.1636AI = \frac{V_{R_1}}{R_1} = \frac{3.6 \, \text{V}}{22 \, \Omega} = 0.1636 \, \text{A}

Step 3: Find the resistance R2R_2.

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Math Problem Analysis

Mathematical Concepts

Circuit Analysis
Ohm's Law
Kirchhoff's Voltage Law

Formulas

V = IR
V_total = V1 + V2

Theorems

Ohm's Law
Kirchhoff's Voltage Law

Suitable Grade Level

College