Electricity And Magnitism, Resistance

$For\quad x\quad number\quad of\quad resistors\quad of\quad resistance\quad 176Ω\quad ,\quad the\quad equivalent\quad \\ resistance\quad of\quad the\quad resistors\quad connected\quad in\quad parallel\quad is\quad given\quad by\quad \\ Ohm’s\quad law\quad as\\ \\ V=IR\\ \\ I=\frac { V }{ R } \\ \\ Supply\quad voltage\quad ,V=220V\quad \\ \\ Current,I=5A\\ \\ Equivalent\quad resistance\quad of\quad the\quad combination=R,\quad given\quad as\\ \\ \frac { 1 }{ R } =x\quad \times \frac { 1 }{ 176 } \\ \\ R=\frac { 176 }{ x } \\ \\ x=\frac { 176\times I }{ V } \\ \\ x=\frac { 176\times 5 }{ 220 } \\ \\ x=\quad 4$

First of all, to solve this question, refer to Wiki based on ohm's law.

Ohm's law - V = IR

=> R = $\frac{V}{I}$ (i)

Given Supply Voltage (V) = 220V

Current (I) = 5A

Let us assume the number of resistors as y.

It is given that the resistors are arranged in parallel. Effective resistance (R[eff]) is given as-

$\frac{1}{R[eff]}$ = $\frac{1}{R1}$ + $\frac{1}{R2}$ ........ $\frac{1}{Ry}$

Here - R1 = R2...... = Ry = 176

$\frac{1}{R[eff]}$ = $\frac{1}{176}$ + $\frac{1}{176}$ ........ $\frac{1}{176}$

$\frac{1}{R[eff]}$ = $\frac{1+1+1..... y times}{176}$

By taking reciprocal of the whole equation, we get -

R[eff] = $\frac{176}{y}$ (ii)

From (i) and (ii) we get -

$\frac{V}{I}$ = $\frac{176}{y}$

y = $\frac{176 * I}{V}$

y = $\frac{176 * 5}{220}$

y = $\frac{880}{220}$

y = 4

y = number of resistors = 4

(1/(1/176+1/176+1/176+1/176)=4.4*10^1)/220=5A