A group of parallel connected heaters draw 24A at 408V. Each heater has a resistance of 187 ohms. How many heaters are in this group?
Understand the Problem
The question describes a circuit with multiple heaters connected in parallel. We are given the total current drawn by the heaters (24A), the voltage across them (408V), and the resistance of each individual heater (187 ohms). We need to determine the total number of heaters in the group.
Answer
11
Answer for screen readers
11
Steps to Solve
- Calculate the current through one heater
Since the heaters are in parallel, the voltage across each heater is the same as the total voltage, which is $408V$. We can use Ohm's Law ($V = IR$) to find the current through one heater: $I = \frac{V}{R}$
- Find the current for one heater
Substitute the values: $V = 408V$ and $R = 187\Omega$
$I = \frac{408}{187} \approx 2.182 A$
- Find the number of heaters
Divide the total current by the current through one heater to find the number of heaters:
$N = \frac{I_{total}}{I_{one\ heater}}$
- Determine the number of heaters based on the formula
$N = \frac{24}{2.182} \approx 11.00$
Since we can't have a fraction of a heater, we round to the nearest whole number.
$N \approx 11$
11
More Information
There are approximately 11 heaters in the group.
Tips
A common mistake is to calculate the total resistance of the parallel circuit first, which is not necessary for solving the problem directly. Also, rounding errors can occur if intermediate calculations are not carried out to sufficient precision.
AI-generated content may contain errors. Please verify critical information
