When three resistors, each having resistance ry are connected in parallel, their resultant resistance is .x. If these three resistances are connected in series, the total resistance will be

When three resistors, each with resistance 'r', are connected in parallel, the reciprocal of the equivalent resistance 'x' is the sum of the reciprocals of the individual resistances [3]. Mathematically, 1/x = 1/r + 1/r + 1/r, which simplifies to 1/x = 3/r, or r = 3x. When these same three resistors are connected in series, the total resistance is the sum of their individual resistances [3]. Therefore, the series resistance Rs = r + r + r = 3r. Substituting the value of 'r' derived from the parallel combination (r = 3x) into the series equation, we get Rs = 3 * (3x) = 9x. Thus, the total resistance in series is nine times the resultant resistance in parallel. Note: Option 3 contains a typo '9*' which represents '9x' in this context.

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.6 > p. 186
2. [3] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.5 > p. 184