Question

Eleven $15\Omega$ and four $7\Omega$ resistors are connected in series. If a new resistance of $21\Omega$ is added in series, the change in the effective resistance would be:

• A.
  $21\Omega$
• B.
  $193\Omega$
• C.
  $234\Omega$
• D.
  $15\Omega$

Answer 1

The correct option is A

$21\Omega$
11 resistors each of resistance $15\Omega$ and 4 resistors each of resistance $7\Omega$ are connected in series.
$⟹$ Effective resistance in series,
$R_{eff}=11\times 15\Omega +4\times 7\Omega =193\Omega$
A new resistor of resistance $21\Omega$ is added to the series.
$⟹$ New effective resistance, $R_{eff}^{\prime }=R_{eff}+21\Omega =193+21=214\Omega$
$\therefore$ Change in effective resiatance =$R_{eff}^{\prime }-R_{eff}=214-193=21\Omega$.