A resistor has a resistance of 176 ohms. How many of these resistors should be connected in parallel so that their combination draws a current of 5 amperes from a 220 volt supply line?

Answer

To solve the problem, we need to determine how many resistors of 176 ohms each should be connected in parallel to draw a total current of 5 amperes from a 220-volt supply. Here’s the step-by-step solution:

### Step 1: Calculate the Equivalent Resistance
We start by using Ohm's Law, which states that \( V = I \times R \), where:
- \( V \) is the voltage (220 volts),
- \( I \) is the current (5 amperes),
- \( R \) is the equivalent resistance (\( R_{AB} \)).

Rearranging the formula gives us:
\[ R_{AB} = \frac{V}{I} = \frac{220 \, \text{volts}}{5 \, \text{amperes}} = 44 \, \text{ohms} \]

### Step 2: Set Up the Parallel Resistance Formula
When resistors are connected in parallel, the equivalent resistance (\( R_{AB} \)) can be calculated using the formula:
\[ \frac{1}{R_{AB}} = \frac{1}{R} + \frac{1}{R} + \cdots + \frac{1}{R} \quad (\text{n times}) \]
Where \( R \) is the resistance of each resistor (176 ohms). This can be simplified to:
\[ \frac{1}{R_{AB}} = \frac{n}{R} \]
Where \( n \) is the number of resistors.

### Step 3: Substitute Known Values
We know:
- \( R_{AB} = 44 \, \text{ohms} \)
- \( R = 176 \, \text{ohms} \)

Substituting these values into the equation gives:
\[ \frac{1}{44} = \frac{n}{176} \]

### Step 4: Solve for \( n \)
To find \( n \), we can rearrange the equation:
\[ n = \frac{176}{44} \]
Calculating this gives:
\[ n = 4 \]

### Conclusion
Thus, **4 resistors** of 176 ohms each should be connected in parallel to draw a current of 5 amperes from a 220-volt supply line.

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