- DASH

Your AI-Powered Personal Tutor

Question

4A

8A

10A

6A

Solution

Please login to view the detailed solution steps...

Go to DASH

© All Rights reserved @ LearnWithDash

Step-by-Step Solution 1. Understanding the Circuit The circuit consists of three resistors connected to a node R whose potential is $V$, and the other ends of these resistors are connected to different potentials or ground. We need to apply Kirchhoff’s Current Law (KCL) at node R to find the current through the 6$\Omega$ resistor. 2. Assigning Node Voltages Let the voltage at node R be $V$. The resistor values and other node voltages are given as follows: A 6$\Omega$ resistor connected from node R to ground (0 V). A 5$\Omega$ resistor connected from node R to 90 V. A 20$\Omega$ resistor connected from node R to 140 V. 3. Applying Kirchhoff's Current Law (KCL) at Node R KCL states that the algebraic sum of currents flowing into and out of a node must be zero. Labeling currents as flowing from node R through each resistor, we can write: $$ \frac{V - 0}{6} + \frac{V - 90}{5} + \frac{V - 140}{20} = 0. $$ 4. Simplifying the Equation Combine the terms over a common denominator (60 in this case): $$ \frac{10V + 12(V - 90) + 3(V - 140)}{60} = 0. $$ Distribute and combine like terms: $$ \frac{10V + 12V - 1080 + 3V - 420}{60} = 0 \\ \frac{25V - 1500}{60} = 0. $$ 5. Solving for $V$ Set the numerator equal to zero to solve for $V$: $$ 25V - 1500 = 0 \quad \Rightarrow \quad 25V = 1500 \quad \Rightarrow \quad V = 60 \text{ V}. $$ 6. Finding the Current through the 6$\Omega$ Resistor The current through the 6$\Omega$ resistor, $I$, is given by Ohm's law: $$ I = \frac{V}{R} = \frac{60}{6} = 10 \text{ A}. $$ 7. Conclusion The current flowing through the 6$\Omega$ resistor in the given circuit is 10 A.

Subject Backlinks

Biology Subject Chemistry Subject Mathematics Subject Physics Subject Subjects Subject

Quiz Backlink

Parent Quiz 745235

Related Question Backlinks

Question 745340 Question 745344 Question 745338 Question 745346 Question 745336 Question 745348 Question 745334 Question 745350 Question 745332 Question 745352 Question 745330 Question 745354 Question 745328 Question 745356 Question 745326 Question 745358 Question 745324 Question 745360 Question 745322 Question 745362