CONCEPT:

Resistance:

• The measurement of the opposition of the flow of electric current  through a  conductor  is called  resistance  of that conductor. It is denoted by  R.

Resistances in parallel:

• When the  terminals of two or more resistances are connected at the same two points  and  the potential difference across them is equal  is called  resistances in parallel.
• The  net resistance/equivalent resistance(R)  of resistances in parallel is given by:

\(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

• Here both resistors R are in parallel combination, therefore the resultant resistance is

\(⇒ \frac{1}{R_{net}} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

\(⇒ \frac{1}{R_{net}} = \frac{1}{{{R}}} + \frac{1}{{{R}}}=\frac{2}{R}\)

\(⇒ R_{net}=\frac{R}{2}\)

As we know, in parallel combination the potential difference across the resistors remains the same. Therefore, according to ohm's law

⇒ V = IRnet

\(⇒ R_{net}=\frac{R}{2}=\frac{V}{I}=\frac{12\times10^3}{100}=120 V\)

⇒ R = 240 Ω 

NOTE :

• Resistances in series:

• When  two or more resistances are connected one after another  such that the  same current flows through them  are called  as resistances in series .
• The  net resistance/equivalent resistance (R)  of resistances in series is given by:
• Equivalent resistance,  R = R 1 + R 2