Question

What is the total current in the circuit if the voltage from the batter is 10 volts?

Answer 1

2 Ohms

Step-by-step explanation:

To calculate the effective resistance of the circuit, we will start with R3 and R5. This resistance are in series, so we can calculate an effective resistance R7 of these two as follows

R7 = R3 + R5

R7 = 5 Ohms + 5 Ohms

R7 = 10 Ohms.

Then, R7 and R4 are in parallel, so the effective resistance of these two is R8 equal t

`\begin{gathered} (1)/(R_8)=(1)/(R_7)+(1)/(R_4) \\ \\ (1)/(R_8)=(1)/(10)+(1)/(5) \\ \\ (1)/(R_8)=(3)/(10) \\ \\ R_8=(10)/(3)\text{ Ohms} \end{gathered}`

Now, R8 and R2 are in series, so the effective resistance is

R9 = R8 + R2

R9 = 10/3 Ohms + 5 Ohms

R9 = 25/3 Ohms

Finally, R9, R1, and R6 are in parallel, so the effective resistance of the circuit is

`\begin{gathered} (1)/(R_e)=(1)/(R_9)+(1)/(R_1)+(1)/(R_6) \\ \\ (1)/(R_e)=(1)/((25)/(3))+(1)/(5)+(1)/(5) \\ \\ (1)/(R_e)=(3)/(25)+(1)/(5)+(1)/(5) \\ \\ (1)/(R_e)=(13)/(25) \\ \\ R_e=1.92\approx2\text{ Ohms} \end{gathered}`

Therefore, the effective resistance to the nearest whole number is 2 Ohms