An ideal inductor is in turn put across 220 V, 50 Hz and 220 V, 100 Hz supplies. The current flowing through it in the two cases will be

Options

A. equal
B. different
C. zero
D. infinite

Explanation

To find the current flowing through an ideal inductor when connected to two different AC supplies (220 V, 50 Hz and 220 V, 100 Hz), we can follow these steps:

### Step 1: Understand the relationship between voltage, current, and inductive reactance
The current flowing through an inductor in an AC circuit is given by the formula:
\[ I = \frac{V}{X_L} \]
where \( I \) is the current, \( V \) is the voltage across the inductor, and \( X_L \) is the inductive reactance.

### Step 2: Calculate the inductive reactance
The inductive reactance \( X_L \) is defined as:
\[ X_L = 2 \pi f L \]
where \( f \) is the frequency and \( L \) is the inductance of the inductor.

### Step 3: Analyze the two cases
1. **For the first case (50 Hz)**:
- Voltage \( V = 220 \, V \)
- Frequency \( f_1 = 50 \, Hz \)
- Inductive reactance:
\[ X_{L1} = 2 \pi (50) L \]
- Current:
\[ I_1 = \frac{220}{X_{L1}} = \frac{220}{2 \pi (50) L} \]

2. **For the second case (100 Hz)**:
- Voltage \( V = 220 \, V \)
- Frequency \( f_2 = 100 \, Hz \)
- Inductive reactance:
\[ X_{L2} = 2 \pi (100) L \]
- Current:
\[ I_2 = \frac{220}{X_{L2}} = \frac{220}{2 \pi (100) L} \]

### Step 4: Compare the currents
Now, we can express the currents in terms of \( L \):
- For 50 Hz:
\[ I_1 = \frac{220}{2 \pi (50) L} \]

- For 100 Hz:
\[ I_2 = \frac{220}{2 \pi (100) L} \]

### Step 5: Determine the relationship between \( I_1 \) and \( I_2 \)
Notice that:
\[ I_1 = \frac{220}{2 \pi (50) L} \]
\[ I_2 = \frac{220}{2 \pi (100) L} \]
From this, we can see that:
\[ I_1 = 2 \times I_2 \]
This means that the current at 50 Hz is twice the current at 100 Hz.

### Conclusion
Thus, the current flowing through the inductor when connected to a 220 V, 50 Hz supply will be greater than the current flowing through it when connected to a 220 V, 100 Hz supply.