Which is not defining the unit of electric current?
Understanding Electric Current Units
Electric current is fundamentally defined as the rate at which electric charge flows through a circuit. The standard unit for electric current in the International System of Units (SI) is the Ampere (A).
Let's analyze the given options to determine which one does not represent a unit of electric current. We can relate the unit of electric current to other fundamental electrical units using definitions and physical laws like Ohm's Law.
Common Units of Electric Current
- Ampere (A): This is the base SI unit for electric current. One ampere is defined as one coulomb of charge passing through a point in one second.
- Coulomb per second (C/s): Based on the definition of current as charge per unit time, $\text{Current} (I) = \frac{\text{Charge} (Q)}{\text{Time} (t)}$. The unit of charge is Coulomb (C) and the unit of time is second (s). Thus, $\text{C/s}$ is a valid unit for electric current.
- Volt per Ohm (V/Ω): According to Ohm's Law, the voltage ($V$) across a resistor is directly proportional to the current ($I$) flowing through it, with the resistance ($R$) as the constant of proportionality: $V = I \times R$. Rearranging this equation, we get $I = \frac{V}{R}$. The unit of voltage is Volt (V) and the unit of resistance is Ohm ($\Omega$). Therefore, $\text{V/Ω}$ is also a valid unit for electric current.
Analyzing the Options
Now let's examine each option provided:
- Option 1: coulomb/sec
As discussed above, this directly follows from the definition of electric current as the rate of flow of charge ($I = Q/t$). The unit of charge is Coulomb (C) and the unit of time is second (s). Thus, Coulomb/sec is a unit of electric current.
- Option 2: Farad-coulomb/sec
Let's look at the units involved. Farad (F) is the unit of capacitance ($C$). Coulomb (C) is the unit of charge ($Q$). Second (s) is the unit of time ($t$). The definition of capacitance is $C = \frac{Q}{V}$, where $V$ is voltage. Thus, the unit of capacitance, Farad, is equivalent to Coulomb/Volt (C/V).
Let's substitute the unit equivalents into the expression "Farad-coulomb/sec":
$$ \frac{\text{Farad} \times \text{Coulomb}}{\text{sec}} = \frac{(\text{Coulomb/Volt}) \times \text{Coulomb}}{\text{sec}} = \frac{\text{Coulomb}^2}{\text{Volt} \times \text{sec}} $$This combination of units ($\text{Coulomb}^2 / (\text{Volt} \times \text{sec})$) does not simplify to the unit of electric current (Coulomb/sec or Ampere). Therefore, Farad-coulomb/sec is not a unit of electric current.
- Option 3: Volt/Ω
From Ohm's Law ($I = V/R$), the unit of current is Volt/Ohm. Thus, Volt/Ω is a unit of electric current.
- Option 4: ampere
Ampere is the standard SI unit of electric current. Thus, ampere is a unit of electric current.
Summary of Units
Let's summarize the units we analyzed in relation to electric current:
| Expression | Unit Analysis | Is it a unit of Electric Current? |
|---|---|---|
| coulomb/sec | $\frac{\text{Charge}}{\text{Time}}$ | Yes (equivalent to Ampere) |
| Farad-coulomb/sec | $\frac{\text{Capacitance} \times \text{Charge}}{\text{Time}} \rightarrow \frac{\text{C/V} \times \text{C}}{\text{s}} \rightarrow \frac{\text{C}^2}{\text{V} \cdot \text{s}}$ | No |
| Volt/Ω | $\frac{\text{Voltage}}{\text{Resistance}}$ (from $I=V/R$) | Yes (equivalent to Ampere) |
| ampere | Base SI Unit | Yes |
Based on this analysis, the option that does not define the unit of electric current is Farad-coulomb/sec.
Important Questions from Basic Electricity
In a series lamp circuit, each bulb is rated for 2 V. Calculate the number of bulbs to be connected in series to run on a 110 V AC line.
For domestic wiring purposes, how are circuits connected?
If the potential difference across the ends of a conductor is halved, what happens to the current flowing through it?
1 kWh is equivalent to:
A choke has characteristics of______
