Question

The product of C and R has units of ​

Answer 1

Step-by-step explanation:

How do you prove that the product of RC has a unit of time (i.e., sec)?

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Buddha Buck

Answered 2 years ago

Let’s take a look at an ideal resistor. An ideal resistor is defined as a component where the voltage across the component V is proportional to the current through the component I , or in other words, Ohm’s Law holds: V=IR , where R is the constant of proportionality, called the resistance.

V=IR can be rewritten as R=VI , which defines the resistance of a resistor as the ratio of the voltage across it to the current passing through it. Current, in turn, is the charge passing through something in a unit time, so we get I=Qt , where Q is charge. This means we can rewrite Ohm’s Law again in terms of charge to get R=VtQ .

Now let’s take a look at an ideal capacitor. An ideal capacitor is defined as a component where the stored charge Q in the capacitor is proportional to the voltage V across the capacitor, or in other words, Q =VC , where C is the constant of proportionality, called the capacitance.

Q=VC can be rewritten as C=QV , which defines the capacitance of a capacitor as the ratio of the charge in the capacitor to the voltage across it.

Multiplying the two together, and you get

RC=(VtQ)(QV)=VQtQV=t

In other words, RC is time.