A DC circuit consists of a resistor of 10 Ω connected across a 20 V supply.With reference to current and power, consider the following statements:1.The current flowing through the resistor is 2 A.2.The power dissipated in the resistor is 40 W.3.If resistance is doubled, current becomes 1 A.4.Power remains unchanged if resistance is doubled.Which of the above statements is/are correct?

Correct Answer: C - 1, 2 and 3 only

Quick Concept Explanation

At fixed supply voltage, doubling resistance halves current and halves power because P=V²/R. Given V=20 V and R=10 Ω: I=V/R=2 A and P=VI=40 W. If R doubles to 20 Ω at the same 20 V, I=1 A and P=20 W. Key relation: I=V/R; P=VI=I²R=V²/R.

Exam focus: At fixed V, power varies inversely with R. Common trap: Do not assume power stays constant when resistance changes on a fixed-voltage source.

Statement-wise Verification

• Statement 1 - Correct.
  The current flowing through the resistor is 2 A.
  Given V=20 V and R=10 Ω: I=V/R=2 A and P=VI=40 W.
• Statement 2 - Correct.
  The power dissipated in the resistor is 40 W.
  Given V=20 V and R=10 Ω: I=V/R=2 A and P=VI=40 W.
• Statement 3 - Correct.
  If resistance is doubled, current becomes 1 A.
  At fixed supply voltage, doubling resistance halves current and halves power because P=V²/R.
• Statement 4 - Incorrect.
  Power remains unchanged if resistance is doubled.
  The correct principle is: At fixed supply voltage, doubling resistance halves current and halves power because P=V²/R.

Core Concept

Resistive DC calculations follow Ohm's law and the power relations P=VI=I²R=V²/R. At fixed supply voltage, doubling resistance halves current and halves power because P=V²/R.

Formula / Key Relationship

I=V/R; P=VI=I²R=V²/R.

Step-by-Step Check

Given V=20 V and R=10 Ω: I=V/R=2 A and P=VI=40 W. If R doubles to 20 Ω at the same 20 V, I=1 A and P=20 W.

Why the Other Options Are Wrong

Option A is incorrect because it omits correct statement(s) 3. Option B is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 1, 3. Option D is incorrect because it includes incorrect statement(s) 4.

Exam Shortcut / Approach

At fixed V, power varies inversely with R.

Common Mistake

Do not assume power stays constant when resistance changes on a fixed-voltage source.

Quick Revision

Resistive DC Circuit Calculations is linked with Ohm's Law and Power, DC Circuits and Basic Electrical Engineering. At fixed V, power varies inversely with R.