Question

Calculate the effective resistance of the following electric circuit.

• A. $\frac{3}{19}\Omega$
• B. $\frac{11}{26}\Omega$
• C. $\frac{15}{28}\Omega$
• D. $\frac{7}{23}\Omega$

Answer 1

The correct option is C $\frac{15}{28}\Omega$

Given circuit diagram:
The three resistors between the nodes A, B and E are in parallel.
$⟹1/R_{eff,1}=1/1+1/1+1/1=3$
$⟹R_{eff,1}=\frac{1}{3}\Omega$ ------ (1)
Similarly, the three resistors between the nodes C, D and E are in parallel.
$⟹R_{eff,2}=\frac{1}{3}\Omega$ ------ (2)
Also the two resistors between E and C are in series.
$⟹R_{eff,3}=1+1=2\Omega$ ----- (3)

$R_{eff,2}$ and $R_{eff,3}$ are in parallel.
$1/R_{eff,4}=1/R_{eff,2}+1/R_{eff,3}=3+1/2=7/2$
$⟹R_{eff,4}=\frac{2}{7}\Omega$ ----- (4)

$R_{eff,1}$ and the resistor between A and E are in parallel.
$1/R_{eff,5}=1/R_{eff,1}+1/1=3+1=4$
$⟹R_{eff,5}=\frac{1}{4}\Omega$ ----- (5)

$\therefore$ Effective resistance of the circuit, $R_{eff}=R_{eff,5}+R_{eff,4}=\frac{1}{4}+\frac{2}{7}=\frac{7+8}{28}$$=\frac{15}{28}\Omega$.