Answer:
The final (equivalent) resistance of the circuit is 5 Ohms.
Explanation:
Use the formulas for combining two resistors
(a) in series [tex]R=R_1+R_2[/tex]
(b) in parallel [tex]\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}[/tex]
Steps:
Start simplifying the circuit at the right end (I am indexing the resistors by the index of the current in the schema)
Step 1: combine resistors 5 and 6 (parallel):
R_A = 1/(1/10+1/30)= 30/4 =15/2 Ohm
Step 2: combine 4 and 7 with R_A (series)
R_B = R4+R_A+R7 = 2 + 15/2 + 1/2 = 10 Ohm
Step 3: Resistor 3 with R_B (parallel):
R_C = 1/(1/15 + 1/10) = 6 Ohm
Step 4: Resistor 2 with R_C (parallel):
R_D = 1/(1/12+1/6) = 4 Ohm
Ste 5 Resistor 1 with R_D (series):
R = 1 + 4 = 5 Ohm
The final (equivalent) resistance of the circuit is 5 Ohms.
