Question

Determine the equivalent resistance and the total current flowing throughthis circuit:

Answer 1

Given:

The resistances: R1 = 25 ohms

R2 = 100 ohms

R3 = 50 ohms

R4 = 75 ohms

R5 = 150 ohms

The battery has a voltage of V = 12 V

The resistances R1 and R2 are connected in parallel and the resistances R4 and R5 are also connected in parallel.

R3 and both the pair of resistances connected in parallel are connected in series.

To find the equivalent resistance and the total current flowing through the circuit.

Step-by-step explanation:

The equivalent resistance of R1 and R2 connected in parallel can be calculated as

`\begin{gathered} (1)/(R_(12))=(1)/(R1)+(1)/(R2) \\ =(1)/(25)+(1)/(100) \\ R_(12)=\text{ 20 }\Omega \end{gathered}`

The equivalent resistance of R4 and R5 connected in parallel can be calculated as

`\begin{gathered} (1)/(R_(45))=(1)/(R4)+(1)/(R5) \\ =(1)/(75)+(1)/(150) \\ R_(45)=\text{ 50 }\Omega \end{gathered}`

The equivalent resistance of R3, R12, and R45 connected in series can be calculated as

`\begin{gathered} R_(eq)=R_(12)+R3+R_(45) \\ =20+50+50 \\ =120\text{ }\Omega \end{gathered}`

The total current flowing through the circuit can be calculated using Ohm's law

`\begin{gathered} V=IR \\ I=(V)/(R) \\ =(12)/(120) \\ =\text{ 0.1 A} \end{gathered}`

Thus, the equivalent resistance of the circuit is 120 ohms and the total current flowing through the resistors is 0.1 A.