Question 23 of 31intermediate🔧 ApplyNumerical3 marks

How many 176 Ω resistors (in parallel) are required to carry 5 A on a 220 V line?

Correct Answer

Given: Resistance of each resistor, R = 176 Ω; Current, I = 5 A; Voltage, V = 220 V.

Step 1: Calculate equivalent resistance needed using Ohm's law: R_eq = V/I = 220 V / 5 A = 44 Ω.

Step 2: For n resistors of equal resistance R in parallel, the equivalent resistance is R_eq = R/n. Solving for n: 44 = 176/n, therefore n = 176/44 = 4.

Answer: 4 resistors of 176 Ω each connected in parallel are required to carry 5 A on a 220 V line.

Exercise: EXERCISES | Q: 10 | (Page Page 23)
For More Understanding

Explanation

This is a numerical problem from the NCERT textbook about parallel resistors. Using Ohm's law, we first find the equivalent resistance needed (44 Ω), then apply the parallel resistance formula to find that 4 resistors of 176 Ω each are needed.

Solution Steps

  1. Step 1: Calculate equivalent resistance needed using Ohm's law: R_eq = V/I = 220 V / 5 A = 44 Ω

  2. Step 2: For n resistors of equal resistance R in parallel, the equivalent resistance is R_eq = R/n

  3. Step 3: Solve for n: 44 = 176/n, therefore n = 176/44 = 4

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