Question

14. Calculate the effective resistance between the points A and B in the circuit given
below.
​

Answer 1

Resistors $\sf{R_8=10\ \Omega}$ and $\sf{R_{10}=2\ \Omega}$ are in series connection, so their effective resistance is,

$\longrightarrow\sf{10\ \Omega+2\ \Omega=12\ \Omega}$

This resistor is in parallel with $\sf{R_9=6\ \Omega,}$ so their effective resistance is,

$\longrightarrow\sf{\dfrac{12\ \Omega\cdot6\ \Omega}{12\ \Omega+6\ \Omega}=4\ \Omega}$

This resistor is in series with $\sf{R_7=8\ \Omega,}$ so their effective resistance is,

$\longrightarrow\sf{4\ \Omega+8\ \Omega=12\ \Omega}$

This resistor is in parallel with $\sf{R_6=6\ \Omega,}$ so their effective resistance is,

$\longrightarrow\sf{\dfrac{12\ \Omega\cdot6\ \Omega}{12\ \Omega+6\ \Omega}=4\ \Omega}$

This resistor is in series with $\sf{R_5=4\ \Omega,}$ so their effective resistance is,

$\longrightarrow\sf{4\ \Omega+4\ \Omega=8\ \Omega}$

This resistor is in parallel with $\sf{R_4=8\ \Omega,}$ so their effective resistance is,

$\longrightarrow\sf{\dfrac{8\ \Omega\cdot8\ \Omega}{8\ \Omega+8\ \Omega}=4\ \Omega}$

This resistor is in series with $\sf{R_3=4\ \Omega,}$ so their effective resistance is,

$\longrightarrow\sf{4\ \Omega+4\ \Omega=8\ \Omega}$

This resistor is in parallel with $\sf{R_2=8\ \Omega,}$ so their effective resistance is,

$\longrightarrow\sf{\dfrac{8\ \Omega\cdot8\ \Omega}{8\ \Omega+8\ \Omega}=4\ \Omega}$

This resistor is in series with $\sf{R_1=6\ \Omega,}$ so their effective resistance is,

$\longrightarrow\sf{4\ \Omega+6\ \Omega=10\ \Omega}$

Therefore, effective resistance between A and B is,

$\longrightarrow\sf{\underline{\underline{R_{AB}=10\ \Omega}}}$