Henry is equivalent to

Options

A. ampere/second
B. ampere second
C. Ohm/second
D. Ohm second

Answer

To determine the equivalent of the unit "Henry," we can analyze the relationships involving inductance, voltage, current, and time. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Definition of Henry
The unit "Henry" (H) is defined as the unit of inductance in the International System of Units (SI). It is used to quantify the self-inductance of a coil or the mutual inductance between two coils.

**Hint:** Remember that inductance relates to how much voltage is induced in a circuit due to a change in current.

### Step 2: Relate Inductance to Voltage and Current
The relationship between voltage (E), inductance (L), and the rate of change of current (di/dt) is given by the formula:
\[ E = L \frac{di}{dt} \]
Where:
- \( E \) is the induced electromotive force (emf) in volts,
- \( L \) is the inductance in henries,
- \( \frac{di}{dt} \) is the rate of change of current in amperes per second.

**Hint:** This formula shows how inductance relates to the change in current over time.

### Step 3: Rearranging the Formula
From the formula \( E = L \frac{di}{dt} \), we can rearrange it to solve for inductance \( L \):
\[ L = \frac{E}{\frac{di}{dt}} \]

**Hint:** Think about what happens to the units when you rearrange this equation.

### Step 4: Substitute Units
We know that:
- Voltage (E) is measured in volts (V),
- Current (i) is measured in amperes (A),
- Time (t) is measured in seconds (s).

Now, substituting the units into the rearranged formula:
\[ L = \frac{\text{Volts}}{\text{Amperes/second}} \]
This can be rewritten as:
\[ L = \text{Volts} \cdot \frac{\text{seconds}}{\text{Amperes}} \]

**Hint:** Consider the definition of a volt in terms of ohms and amperes.

### Step 5: Express Volts in Terms of Ohms and Amperes
Using Ohm's law, we know that:
\[ 1 \text{ Volt} = 1 \text{ Ohm} \cdot 1 \text{ Ampere} \]
Thus, substituting this into our expression for \( L \):
\[ L = \text{Ohms} \cdot \text{seconds} \]

**Hint:** This step helps to clarify the relationship between the units of inductance and other electrical units.

### Conclusion
Therefore, the unit "Henry" is equivalent to:
\[ 1 \text{ H} = 1 \text{ Ohm} \cdot 1 \text{ second} \]

### Final Answer
Henry is equivalent to Ohm-seconds (Ω·s).

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