If a 5.5 $\mathrm { k } \Omega$, 22 $\mathrm { k } \Omega$ and 500$\Omega$resistor are connected in parallel, what is RT ?
A) 28.1 $\mathrm { k } \Omega$
B) 449$\Omega$
C) 330$\Omega$
D) 27.6 $\mathrm { k } \Omega$

Question

If a  5.5  $\mathrm { k } \Omega$, 22 $\mathrm { k } \Omega$ and  500$\Omega$resistor are connected in parallel, what is  RT  ?
A)  28.1  $\mathrm { k } \Omega$
B)  449$\Omega$
C)  330$\Omega$
D)  27.6 $\mathrm { k } \Omega$

Quizplus · Accepted Answer

When resistors are connected in parallel, the equivalent resistance (RT) is given by the formula:

$$\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...$$

where R1, R2, R3, ... are the resistances of individual resistors.

Substituting the given values:

$$\frac{1}{R_T}=\frac{1}{5500}+\frac{1}{22000}+\frac{1}{500}$$

$$\frac{1}{R_T}=\frac{1}{5500}+\frac{1}{22000}+\frac{44}{22000}$$

$$\frac{1}{R_T}=\frac{1}{5500}+\frac{45}{22000}$$

$$\frac{1}{R_T}=\frac{1}{5500}+\frac{1}{489}$$

$$\frac{1}{R_T}=\frac{66}{27045}$$

$$R_T=\frac{27045}{66}$$

$$R_T=409.09\Omega$$

Thus, the correct option is B) 449$\Omega$ (which is the closest value to 409.09$\Omega$).

If a 55 kΩ\mathrm { k } \OmegakΩ , 22 kΩ\mathrm { k } \OmegakΩ

If a 55 $\mathrm { k } \Omega$ , 22 $\mathrm { k } \Omega$