An electric motor has an effective resistance of 61.0 `Omega` and an inductive reactance of 52.0 `Omega` when working under load. The rms voltage across the alternating source is 420 V. Calculate the rms current.

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the given values
- Effective resistance (R) = 61.0 Ω
- Inductive reactance (X_L) = 52.0 Ω
- RMS voltage (V) = 420 V

### Step 2: Calculate the impedance (Z)
The impedance in an AC circuit with resistance and inductive reactance is given by the formula:
\[ Z = \sqrt{R^2 + X_L^2} \]

Substituting the given values:
\[ Z = \sqrt{(61.0)^2 + (52.0)^2} \]
\[ Z = \sqrt{3721 + 2704} \]
\[ Z = \sqrt{6425} \]
\[ Z \approx 80.15 \, \Omega \]

### Step 3: Calculate the RMS current (I_RMS)
The RMS current can be calculated using Ohm's law for AC circuits:
\[ I_{RMS} = \frac{V}{Z} \]

Substituting the known values:
\[ I_{RMS} = \frac{420 \, V}{80.15 \, \Omega} \]
\[ I_{RMS} \approx 5.24 \, A \]

### Final Answer
The RMS current is approximately **5.24 A**.

---