Understanding the SI Unit of Electric Charge

The question asks us to find the correct expression for the SI unit of electric charge, known as the Coulomb (symbolized as $C$), in terms of other basic or derived SI units. Electric charge is a fundamental physical property that underlies the electromagnetic force. The Coulomb is the standard unit used to quantify this property within the International System of Units (SI).

Evaluating Unit Expressions for Coulomb

We need to carefully examine each provided option to determine which one accurately represents the Coulomb ($C$) using established physics principles and unit definitions.

Option 1: Watt / Ampere ($W/A$)

• The Watt ($W$) is the SI unit for power, which measures the rate of energy transfer or conversion. Power ($P$) is related to voltage ($V$) and current ($I$) by the formula $P = V \times I$.
• The Ampere ($A$) is the SI unit for electric current, representing the flow rate of charge.
• From the relationship $P = V \times I$, we can express the units as $W = V \times A$.
• Therefore, the unit expression $W/A$ simplifies to $(V \times A) / A$, which equals $V$.
• The unit $V$ represents the Volt, the SI unit of electric potential difference, not electric charge. Hence, this option is incorrect.

Option 2: Farad / Volt ($F/V$)

• The Farad ($F$) is the SI unit of electrical capacitance. Capacitance ($C_{cap}$) is defined as the ratio of electric charge ($Q$) stored on a conductor to the difference in electric potential ($V$) across it: $C_{cap} = Q/V$.
• The Volt ($V$) is the SI unit of electric potential difference.
• Using the definition of capacitance, the unit relationship is $F = C/V$.
• When we divide Farads by Volts ($F/V$), we get $(C/V) / V$, which simplifies to $C/V^2$.
• This unit (Coulomb per Volt squared) is not equivalent to the Coulomb ($C$). Hence, this option is incorrect.

Option 3: Joule $\cdot$ Volt ($J \cdot V$)

• The Joule ($J$) is the SI unit of energy or work.
• The Volt ($V$) is the SI unit of electric potential difference. Potential difference is defined as the work done per unit charge: $V = \text{Work}/\text{Charge}$ or $V = J/C$.
• This implies that the unit relationship is $J = C \cdot V$.
• Multiplying Joules by Volts ($J \cdot V$) gives us $(C \cdot V) \cdot V$, which equals $C \cdot V^2$.
• This unit combination (Coulomb times Volt squared) does not represent electric charge. Hence, this option is incorrect.

Option 4: Ampere $\cdot$ second ($A \cdot s$)

• The Ampere ($A$) is the SI unit of electric current. Current ($I$) is fundamentally defined as the rate at which electric charge ($Q$) flows through a surface per unit time ($t$): $I = Q/t$.
• The second ($s$) is the SI unit of time.
• By rearranging the definition of current, we can express electric charge as the product of current and time: $Q = I \times t$.
• Consequently, the SI unit of electric charge can be expressed as the product of the unit of current (Ampere, $A$) and the unit of time (second, $s$).
• This yields the unit expression $A \cdot s$.
• By definition, one Coulomb ($1 C$) is the amount of electric charge transported by a constant current of one Ampere ($1 A$) in one second ($1 s$). Therefore, $1 C = 1 A \cdot s$.
• This option correctly represents the SI unit of electric charge. Hence, this option is correct.

Final Determination of the Correct Unit Expression

After evaluating each option based on the fundamental definitions of SI units in electricity and physics, the expression Ampere $\cdot$ second ($A \cdot s$) is the only one that accurately represents the SI unit of electric charge, the Coulomb ($C$).