Question

(a) What is the resistance of ten$\mathbf{275}\mathbf{-}\mathbf{\Omega }$resistors connected in series? (b) In parallel?

Short answer

(a)The resistance of ten $275\Omega$resistors connected in series is $2750\Omega$.

(b)The resistance of ten$275\Omega$ resistors connected in parallel is $27.50\Omega$.

Step-by-step solution

Definition of resistance in series and parallel

An unwillingness to accept anything, such as a change or a new thought, is known as resistance.

Resistance in series: When resistors are daisy-chained together in a single line and a common current flows through them, they are said to be connected in series.

Resistance in parallel: In a parallel circuit, the total resistance is always less than any of the branch resistances. The total resistance in the circuit decreases when more parallel resistances are added to the lines.

Finding resistance of resistors connected in series

(a)

The equivalent resistance of the n resistors with each of resistance and connected in series can be expressed as,

${\mathrm{R}}_{\mathrm{s}}=\mathrm{nR}$

Therefore, substituting the given data, we will get,

$$\begin{gathered} R_s=10\times 275 \\ =2750\Omega \end{gathered}$$

Thus, the resistance of ten $275\Omega$resistors connected in series is $2750\Omega$.

Finding resistance of resistors connected in parallel

(b)

The equivalent resistance of the n resistors with each of resistance and connected in parallel can be expressed as,

${\mathrm{R}}_{\mathrm{P}}=\frac{\mathrm{R}}{\mathrm{n}}$

Therefore, substituting the given data, we will get,

$$\begin{gathered} {\mathrm{R}}_{\mathrm{P}}=\frac{275\mathrm{\Omega }}{10} \\ =27.50\mathrm{\Omega } \end{gathered}$$

Hence, the resistance of ten$275\Omega$resistors connected in parallel is$27.50\Omega$.