Let's break down and solve the problem step by step using the given information and formulas. --- ## **Step 1: List the Given Data** - **Supply voltage, \( V_1 \) = 230 V** - **Secondary turns, \( N_2 \) = 120** - **Frequency, \( f \) = 50 Hz** (from the formula context) - **Inductance, \( L_1 \) = .5 H** (from substitution step) - **Formula for no-load current:** \( I_ = \frac{V_1}{2\pi f L_1} \) --- ## **Step 2: Substitute Values for No-load Current** Using: \[ I_ = \frac{V_1}{2\pi f L_1} \] Substitute the values: - \( V_1 = 230 \) V - \( f = 50 \) Hz - \( L_1 = .5 \) H \[ I_ = \frac{230}{2\pi \times 50 \times .5} \] --- ## **Step 3: Calculate the Denominator** Calculate \( 2\pi \times 50 \times .5 \): - \( 2\pi = 6.2832 \) - \( 6.2832 \times 50 = 314.16 \) - \( 314.16 \times .5 = 157.08 \) --- ## **Step 4: Calculate No-load Current \( I_ \)** \[ I_ = \frac{230}{157.08} \] \[ I_ \approx 1.464 \text{ A} \] --- ## **Step 5: Write the Final Answer** ### **Final Answer** \[ \boxed{I_ \approx 1.46 \text{ A}} \] --- ### **Explanation** - The no-load current (\(I_\)) is the current drawn by the primary winding of a transformer when the secondary is open (no load). - It is calculated using the primary voltage, frequency, and inductance. - Here, the answer is approximately **1.46 A**. --- **If you need to calculate the secondary voltage using the turns ratio, provide the value of \(N_1\) (primary turns) to proceed further!**