Let's solve the problem step by step: ### **Step 1: Identify What is Being Asked** We are asked to calculate the current through the first branch (`I1`) that contains resistor `R1 = 120 Ω` with a voltage source of `V = 12V`. --- ### **Step 2: Use Ohm's Law** For resistors in parallel, each branch gets the full source voltage: \[ I_1 = \frac{V}{R_1} \] Where: - \(V = 12V\) - \(R_1 = 120\,\Omega\) --- ### **Step 3: Substitute and Calculate** \[ I_1 = \frac{12V}{120\,\Omega} = 0.1A \] --- ### **Step 4: Analyze the Options** #### (a) "I * 1 = V/R1 11-1 A" - **Explanation:** Looks like a typo and calculation is not clear, but if you use \(I_1 = V/R_1\), it should be \(0.1A\). The value "11-1 A" is not correct. #### (b) "I * 1 = 1.5A" - **Explanation:** Calculated current is **not** 1.5A. If you do \(12V/120Ω\), you get \(0.1A\), not \(1.5A\). So, this option is incorrect. #### (c) "I * 1 = 3A" - **Explanation:** Calculated current is **not** 3A. This would only be true if the resistance were much smaller (\(12V/4Ω = 3A\)), but our resistance is 120Ω. So, this is incorrect. #### (d) "No answer text provided." - **Explanation:** There is no answer to evaluate. --- ## **Final Answer** **None of the options is correct** as written, but the correct current through the first branch is: \[ \boxed{0.1\,A} \] --- ### **Summary Table** | Option | Value Given | Correct? | Why? | |--------|-------------|----------|------| | (a) | 11-1 A (unclear) | ❌ | Incorrect calculation, should be 0.1A | | (b) | 1.5A | ❌ | Not matching calculation | | (c) | 3A | ❌ | Not matching calculation | | (d) | No answer text | ❌ | No value provided | **Explanation:** The current through \( R_1 \) is \( I_1 = \frac{12V}{120Ω} = 0.1A \). All other values are incorrect for this setup.

# Calculation of Current through the First Branch Given: - \( R_1 = 12\,\Omega \) - \( R_2 = 24\,\Omega \) - Voltage source \( V = 12\,V \) --- ## Step 1: Identify the Circuit Connection - The problem appears to involve resistors in parallel with the source, as indicated by the previous context. - Since the question asks for the current passing through the first branch (\( R_1 \)), and both resistors are connected across the same voltage source, they are in parallel. --- ## Step 2: Apply Ohm's Law For resistors in parallel, each resistor experiences the full source voltage: \[ I_1 = \frac{V}{R_1} \] \[ I_2 = \frac{V}{R_2} \] --- ## Step 3: Calculate the Current through \( R_1 \) \[ I_1 = \frac{12\,V}{12\,\Omega} = 1\,A \] Similarly, for completeness, \[ I_2 = \frac{12\,V}{24\,\Omega} = 0.5\,A \] --- ## **Final Answer:** \[ \boxed{ \text{Current through } R_1 = 1\,A } \] --- ## **Summary** | Resistor | Resistance | Voltage | Current Calculation | Current | |------------|--------------|---------|---------------------|---------| | \( R_1 \) | 12 Ω | 12 V | \( 12V/12\Omega \) | 1 A | | \( R_2 \) | 24 Ω | 12 V | \( 12V/24\Omega \) | 0.5 A | --- ## **Note** - The current through \( R_1 \) is **1 A**. - This is valid only if both resistors are connected directly across the 12 V source in parallel. --- **No options were provided in your message, but based on this calculation, the current through \( R_1 \) is 1 A.**