Given:
Two circuits with multiple resistors
To find:
The net resistance of the circuits
Explanation:
For the first circuit
The equivalent series resistance of the 1 and 2 is,
[tex]\begin{gathered} R_1+R_2 \\ =20+16 \\ =36\text{ ohm} \end{gathered}[/tex]The equivalent series resistance of the 4 and 5 is,
[tex]\begin{gathered} 10+14 \\ =24\text{ ohm} \end{gathered}[/tex]The net resistance of the resistances is,
[tex]\begin{gathered} \frac{1}{R}=\frac{1}{36}+\frac{1}{24}+\frac{1}{12} \\ \frac{1}{R}=\frac{11}{72} \\ R=\frac{72}{11}\text{ohm} \\ R=6.54\text{ ohm} \end{gathered}[/tex]Hence, the net resistance of the upper circuit is 6.54 ohms.
For the circuit below:
[tex]R_2,\text{ R}_3,\text{ R}_4\text{ are in series}[/tex]So, the equivalent resistance is,
[tex]\begin{gathered} R_2+R_3+R_4 \\ =2+2+2 \\ =6\text{ ohm} \end{gathered}[/tex]This equivalent resistance in parallel with
[tex]R_5[/tex]So, the equivalent resistance is,
[tex]\begin{gathered} \frac{6\times2}{6+2} \\ =1.5\text{ ohm} \end{gathered}[/tex]Now 1.5 ohm is in series with the rest two resistances.
So, the net resistance is,
[tex]\begin{gathered} R_1+R_6+1.5 \\ =2+2+1.5 \\ =5.5\text{ ohm} \end{gathered}[/tex]Hence, the net resistance of the circuit below is 5.5 ohms.
