When current (I) in R-L series circuit is constant where L is a pure inductor, The following statements are given

Options

A. voltage across R is RI.
B. voltage across L is equal to voltage across R.
C. voltage across L is equal to supply voltage.
D. magnetic energy stored is `1/2Li^2`

Answer

To analyze the statements regarding an R-L series circuit where the current (I) is constant, we will evaluate each statement step by step.

### Step-by-Step Solution:

1. **Understanding the Circuit**:
In an R-L series circuit, a resistor (R) and an inductor (L) are connected in series with a voltage supply. When the current is constant, it means that the circuit has reached a steady state.

2. **Voltage Across the Resistor (R)**:
According to Ohm's Law, the voltage across the resistor (V_R) can be calculated as:
\[ V_R = I \cdot R \]
Since the current (I) is constant, this statement is **correct**.

3. **Voltage Across the Inductor (L)**:
The voltage across the inductor (V_L) in a series circuit is given by:
\[ V_L = L \frac{dI}{dt} \]
However, since the current is constant, \(\frac{dI}{dt} = 0\). Therefore, the voltage across the inductor is:
\[ V_L = L \cdot 0 = 0 \]
This means that the voltage across the inductor is not equal to the voltage across the resistor. Hence, the statement that "L is equal to voltage across R" is **incorrect**.

4. **Total Supply Voltage**:
The total supply voltage (V_s) in the circuit is the sum of the voltages across the resistor and the inductor:
\[ V_s = V_R + V_L \]
Since \(V_L = 0\) when the current is constant, we have:
\[ V_s = V_R = I \cdot R \]
Therefore, the supply voltage is equal to the voltage across the resistor.

5. **Magnetic Energy Stored in the Inductor**:
The magnetic energy (U) stored in an inductor is given by the formula:
\[ U = \frac{1}{2} L I^2 \]
This statement is **correct** as it represents the energy stored in the magnetic field of the inductor when current I flows through it.

### Summary of Statements:
- **Statement 1**: Voltage across resistance R is correct (True).
- **Statement 2**: L is equal to voltage across R is incorrect (False).
- **Statement 3**: Voltage across L is equal to supply voltage is incorrect (False).
- **Statement 4**: The magnetic energy stored in the inductor is \(\frac{1}{2} L I^2\) is correct (True).

### Final Answers:
The correct statements are 1 and 4.

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