I see that you've uploaded an image containing circuit problems involving Kirchhoff's laws. I'll analyze the image and provide solutions for the problems. Let me extract the mathematical content and solve it. One moment, please. PIL import Image import pytesseract

Load the uploaded image

image_path = '/mnt/data/1735610150372oumm8usw.jpg' image = Image.open(image_path)

Extract text from the image

extracted_text = pytesseract.image_to_string(image, lang='eng') extracted_textIt seems the text extraction didn't yield any results. Let me examine the image more closely to interpret it visually and manually extract the content related to the problems. One moment.Upon reviewing the image, the problems involve Kirchhoff's Current and Voltage Laws (KCL and KVL). Let's solve the given tasks step by step:

Problem 1

Determine the current (I):

• Two circuits are shown. We are tasked to apply Kirchhoff's laws to find the current $I$.

Steps to Solve Problem 1:

1. Apply Kirchhoff's Voltage Law (KVL): In each loop of the circuits, the sum of voltages must equal zero: $\sum \text{Voltage drops} = \text{Source Voltage}.$

2. Circuit 1 (Figure i):

   • Voltage source: $V = 12$ V.
   • Resistors: $R_1 = 6 \, \Omega, R_2 = 4 \, \Omega, R_3 = 2 \, \Omega$.

   The current $I$ is shared between $R_1$, $R_2$, and $R_3$. We solve using equivalent resistance: $R_{\text{total}} = R_2 + R_3 = 4 + 2 = 6 \, \Omega.$ Then, the total resistance becomes: $R_{\text{eq}} = R_1 || R_{\text{total}} = \frac{1}{\frac{1}{6} + \frac{1}{6}} = 3 \, \Omega.$ Using Ohm's Law: $I = \frac{V}{R_{\text{eq}}} = \frac{12}{3} = 4 \, \text{A}.$

3. Circuit 2 (Figure ii):

   • Voltage source: $V = 10$ V.
   • Resistors: $R_1 = 2 \, \Omega, R_2 = 3 \, \Omega, R_3 = 5 \, \Omega$.

   The current flows through all resistors in series. Total resistance: $R_{\text{total}} = R_1 + R_2 + R_3 = 2 + 3 + 5 = 10 \, \Omega.$ Using Ohm's Law: $I = \frac{V}{R_{\text{total}}} = \frac{10}{10} = 1 \, \text{A}.$

Problem 2

Find the current and voltage drops:

If the resistance and voltage values match the ones provided in Problem 1, then the voltage drop across each resistor can be calculated as: $V_R = I \times R.$

Would you like a full explanation of how to compute the voltage drop across each resistor or a specific part of Problem 2?