Math Problem Statement
solve using nodal
Solution
To solve for the current using Nodal Analysis, let us systematically proceed as follows.
Step 1: Define Node Voltages
Let:
- = voltage at node (common node between , , and ).
Step 2: Write KCL at Node
By Kirchhoff's Current Law (KCL), the sum of currents entering or leaving the node is zero. Assume the currents flow out of node :
Substitute the values into the KCL equation:
Step 3: Simplify the Equation
Combine the terms:
To eliminate fractions, find the LCM of the denominators , which is . Multiply through by :
Simplify each term:
Expand:
Combine like terms:
Solve for :
Step 4: Solve for
The current flows through resistor , and it is given by Ohm's Law:
Substitute , , and :
Convert to milliamps (mA):
Final Answer:
The current is 30 mA.
Do you need a detailed breakdown of any step? Let me know!
Here are related questions for practice:
- What is the current through and ?
- Verify the voltage at node using KCL.
- How would the current change if is doubled?
- Solve for the power dissipated in each resistor.
- How would the solution change if ?
Tip: Always double-check units when solving for current and voltage in circuit analysis!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Nodal Analysis
Kirchhoff's Current Law (KCL)
Ohm's Law
Formulas
Kirchhoff's Current Law: ΣI = 0
Ohm's Law: I = V / R
Theorems
Kirchhoff's Current Law
Ohm's Law
Suitable Grade Level
Undergraduate Engineering or Grades 11-12 Physics
Related Recommendation
Find the Current i3 in a Series Circuit with Two Voltage Sources
Calculate Current i3 in a Series-Parallel Circuit Using Kirchhoff’s Laws
Calculate Current I2 Using Kirchhoff's Law and Ohm's Law
Solving for I3 Using Kirchhoff's Current Law
Kirchhoff's Laws: Calculate Currents in a Circuit with Two Voltage Sources