Question

A heating element is marked ${{210 V, 630 V}}$. Find the resistance of the element when connected to $210{{ V}}$ dc source.

Answer 1

Hint: First of all, write the given quantities. For finding the resistance of the element, use the formula ${{R = }}\dfrac{{{{{V}}^{{2}}}}}{{{P}}}$ where ${{R = }}$resistance of the electronic component and ${{P = }}$ power of the electronic component. Then substitute the given values in the above formula and the value of resistance can be obtained.

Complete step by step solution:
Given: Voltage of a heating element, ${{V = 210 V}}$
Power of a heating element, ${{P = 630 V}}$
To find: Resistance of the heating element
Basically, the electrical resistance measures the amount of flow of electric charge restricted in the circuit. Conductors have low value of resistivity but insulators have high value of resistivity. The opposite of resistivity is conductivity. Conductors have high value of resistivity and low value of conductivity.
The S.I. unit of resistance is ohm (represented by Greek letter omega $\Omega $ )
The S.I. unit of resistivity is mho (represented by ${\Omega ^{ - 1}}$ )
The S.I. unit of power is Watt (represented by W)
The S.I. unit of voltage (potential difference) is V. Both the representation and the S.I. unit of potential difference is same i.e. V.
Formula for resistance is given as
${{R = }}\dfrac{{{{{V}}^{{2}}}}}{{{P}}}$
On substituting the given values, the value of resistance ${{R}}$becomes
${{R = }}\dfrac{{{{\left( {{{210}}} \right)}^{{2}}}}}{{{{630}}}}{{ = 70 }}\Omega $

Therefore, the value of resistance will be $70{{ }}\Omega $.

Note: There are many formulae for finding the resistance of an electronic component. But in relation to the given quantities i.e. voltage and power. The best suitable formula is given by ${{R = }}\dfrac{{{{{V}}^{{2}}}}}{{{P}}}$. Keep in mind that, use the suitable formula according to the question in order to find the simple (with less complexions) and to the point solution.