To solve this circuit problem, we need to find the total resistance of the entire circuit and then use Ohm's Law to find the total current flowing from the battery.
Here is the step-by-step breakdown:
Step 1: Simplify the Parallel Resistors
First, look at the three resistors on the right side (20Ω, 12Ω, and 25Ω). They are connected in parallel. We need to calculate their equivalent resistance ($R_p$).
The formula for parallel resistance is:
$$ \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} $$
Plug in the values:
$$ \frac{1}{R_p} = \frac{1}{20} + \frac{1}{12} + \frac{1}{25} $$
To add these fractions, find a common denominator. The least common multiple for 20, 12, and 25 is 300.
* $\frac{1}{20} = \frac{15}{300}$
* $\frac{1}{12} = \frac{25}{300}$
* $\frac{1}{25} = \frac{12}{300}$
Add them together:
$$ \frac{1}{R_p} = \frac{15 + 25 + 12}{300} = \frac{52}{300} $$
Now, flip the fraction to solve for $R_p$:
$$ R_p = \frac{300}{52} \approx 5.77 \, \Omega $$
Step 2: Calculate Total Resistance
Now that we have the equivalent resistance for the parallel part ($5.77 \, \Omega$), we treat it as a single resistor in series with the $40 \, \Omega$ resistor on the left.
$$ R_{total} = R_{series} + R_p $$
$$ R_{total} = 40 \, \Omega + 5.77 \, \Omega $$
$$ R_{total} = 45.77 \, \Omega $$
Step 3: Calculate Total Current
Finally, use Ohm's Law ($I = \frac{V}{R}$) to find the total current flowing through the circuit. The voltage ($V$) is 120 V.
$$ I = \frac{120 \, V}{45.77 \, \Omega} $$
$$ I \approx 2.62 \, A $$
Final Answer:
The total current in the circuit is approximately
2.62 Amps.
Parent Tip: Review the logic above to help your child master the concept of ohms law practice worksheet.
