Using Kirchhoff’s Laws On A Complex Circuit

Show/Hide Sub-topics (D.C. Circuits | A Level Physics)

The picture above shows a “bridge” circuit. Find the current in each resistor and the equivalent resistance of the network of five resistors. Find the potential difference $V_{ab}$

Loop 1:

\begin{aligned} 13 &= I_{1} + (I_{1} – I_{3}) \\ 2 I_{1} – I_{3} &= 13 \end{aligned}

Loop 2:

\begin{aligned} 13 &= I_{2} + 2(I_{2} + I_{3}) \\ 3 I_{2} + 2I_{3} &= 13 \end{aligned}

Loop 3:

\begin{aligned} 0 &= -I_{1} – I_{3} + I_{2} \\ I_{1} – I_{2}&=- I_{3} \end{aligned}

Solving the above equations:

\begin{aligned} I_{1} &= 6 \, \text{A} \\ I_{2} &= 5 \, \text{A} \\ I_{3} &= -1 \, \text{A} \\ R_{eq} &= \frac{13}{11} \, \Omega \end{aligned}

Mini Physics

As the Administrator of Mini Physics, I possess a BSc. (Hons) in Physics. I am committed to ensuring the accuracy and quality of the content on this site. If you encounter any inaccuracies or have suggestions for enhancements, I encourage you to contact us. Your support and feedback are invaluable to us. If you appreciate the resources available on this site, kindly consider recommending Mini Physics to your friends. Together, we can foster a community passionate about Physics and continuous learning.

This site uses Akismet to reduce spam. Learn how your comment data is processed.