If C and R denote capacitance and resistance., the dimensional formula of CR is

The correct option is [M⁰L⁰T¹].

To find the dimensional formula of the product of capacitance and resistance, we can derive it step-by-step from their fundamental physical definitions.

Step 1: Understand Capacitance

Capacitance is defined as the ratio of electric charge to potential difference:

$C=\frac{Q}{V}$

where:

$C$

is the capacitance,

$Q$

is the electric charge, and

$V$

is the potential difference.

Step 2: Understand Resistance

According to Ohm's law, resistance is the ratio of potential difference to electric current:

$R=\frac{V}{I}$

where:

$R$

is the resistance, and

$I$

is the electric current.

Step 3: Calculate the Product of Capacitance and Resistance

Now, we multiply the formula for capacitance by the formula for resistance:

$C\times R=\left(\frac{Q}{V}\right)\times \left(\frac{V}{I}\right)$

By canceling out the potential difference term,

$V$

from the numerator and denominator, we get:

$CR=\frac{Q}{I}$

Step 4: Relate Charge and Current to Time

Electric current is the rate of flow of charge over time:

$I=\frac{Q}{t}$

which can be rewritten as:

$Q=I\times t$

where:

$t$

represents time. Substituting this expression for charge into our product equation gives:

$CR=\frac{I\times t}{I}$

Canceling the current term,

$I$

we find:

$CR=t$

Step 5: Determine the Dimensional Formula

Since the product of capacitance and resistance simplifies directly to time, its dimension is that of time:

$\left[CR\right]=\left[T\right]$

Expressing this in the standard mass (M), length (L), and time (T) format, we write:

[M⁰L⁰T¹]