L/Rhas dimensions same as that ofa)Reactanceb)Capacitancec)Resistanced)TimeCorrect answer is option 'D'. Can you explain this answer?

Question

L/Rhas dimensions same as that of&#8203;a)Reactanceb)Capacitancec)Resistanced)TimeCorrect answer is option 'D'. Can you explain this answer?

Answer

First of all we have to find out dimension of L and R .

We know, relation L answer energy is E = 1/2Li^2

so, dimension of L = dimension of energy/dimension of i2

= [ML2T⁻2]/[A2] = [ML2T⁻2A⁻2]

Similarly we know, relation between R and energy is E = i2Rt

So, dimension of R = dimension of E/dimension of i2t

= [ML2T⁻2][A2T] = [ML2T⁻2A⁻2]

Now, dimension of L/R = dimension of L/dimension of R

= [ML2T⁻2A⁻2][ML2T⁻2A⁻2] = [T]

Hence, answer is [T]

Answer

We know, relation L answer energy is E = 1/2Li² so, dimension of L = dimension of energy/dimension of i²= [ML²T⁻²]/[A²] = [ML²T⁻²A⁻²].                                  Similarly we know, relation between R and energy is E = i²Rt   So, dimension of R = dimension of E/dimension of i²t= [ML²T⁻²][A²T] = [ML²T⁻³A⁻²].                                  Now, dimension of L/R = dimension of L/dimension of R= [ML²T⁻²A⁻²][ML²T⁻³A⁻²] = [T].                                 Hence, answer is [T]Hope it helps!!!!!

Answer

Dimensions of L/R:

The dimensions of L/R are the same as that of time.

Explanation:

Inductance (L), resistance (R), and capacitance (C) are fundamental electrical properties that are used to describe the behavior of electrical circuits. Each of these properties has a specific unit of measurement and dimensions.

1. Reactance:
Reactance is a property of inductive (XL) or capacitive (XC) elements in a circuit and is measured in ohms (Ω). The reactance of an inductor (XL) is given by the formula XL = 2πfL, where f is the frequency of the circuit and L is the inductance. The dimensions of reactance are [M^1L^2T^-3I^-2], where M represents mass, L represents length, T represents time, and I represents electric current.

2. Capacitance:
Capacitance (C) is a measure of a capacitor's ability to store electrical energy and is measured in farads (F). The capacitance of a capacitor is given by the formula C = Q/V, where Q is the charge stored on the capacitor and V is the voltage across the capacitor. The dimensions of capacitance are [M^-1L^-2T^4I^2].

3. Resistance:
Resistance (R) is a measure of how much a material or device opposes the flow of electric current and is measured in ohms (Ω). The resistance of a resistor is given by Ohm's Law, which states that R = V/I, where V is the voltage across the resistor and I is the current flowing through it. The dimensions of resistance are [M^1L^2T^-3I^-2].

4. Time:
Time is a fundamental physical quantity and is measured in seconds (s). The dimensions of time are [M^0L^0T^1I^0].

Comparing the dimensions of reactance, capacitance, resistance, and time, we can see that only the dimensions of time match with the dimensions of L/R. Therefore, the correct answer is option 'D' - Time.

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