Question

Derive dimension formula for charge

Answer 1

Derivation

Electric charge (Q) = current × time . . . . (1)

The dimensional formula of,

Current = [I1] . . . . (2)

Time = [T1] . . . . (3)

From equation (1), (2) and (3) we get,

Since, electric charge = current × time

Or, Q = [I1] × [T1] = [T1 I1]

Therefore, the electric charge is dimensionally represented as [M0 L0 T1 I1].

Answer 2

SoLuTiOn :

➡ Given :

✏ A physical quantity charge is provided in the question.

➡ To Find:

✏ Dimension formula of charge.

➡ Formula:

✏ Relation between charge and current is given by

$\huge \star \: \underline{ \huge \boxed{ \bold{ \rm{ \pink{q = I \times t}}}}} \: \huge{ \star}$

➡ Terms indication:

✏ q denotes charge.

✏ I denotes current.

✏ t denotes time.

➡ Calculation:

✏ Dimension formula of current is $[A^{1}]$

✏ Dimension formula of time is $[T^{1}]$

✏ Therefore Dimension formula of charge is given by

✏ $\underline{\boxed{\bold{\rm{\purple{q = [A^{1}T^{1}]}}}}}$

➡ Additional information:

• Current and time are fundamental quantities.
• Charge is a derived quantity.