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?
Answer & step-by-step solution
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.
एक DC परिपथ में 20 V सप्लाई के पार 10 Ω का प्रतिरोधक जुड़ा है।
करंट और शक्ति के संदर्भ में निम्नलिखित कथनों पर विचार कीजिए:
1. प्रतिरोधक से बहने वाला करंट 2 A है।
2. प्रतिरोधक में व्यय शक्ति 40 W है।
3. प्रतिरोध दोगुना करने पर करंट 1 A हो जाता है।
4. प्रतिरोध दोगुना करने पर शक्ति अपरिवर्तित रहती है।
उपरोक्त में से कौन-सा/से कथन सही है/हैं?
उत्तर और चरणबद्ध हल
V=20 V, R=10 Ω: I=V/R=2 A और P=VI=40 W। समान 20 V पर R को 20 Ω करने से I=1 A और P=20 W हो जाता है। मुख्य संबंध: P=VI=I²R=V²/R।
परीक्षा फोकस: स्थिर V पर शक्ति R के व्युत्क्रमानुपाती होती है। सामान्य गलती: प्रतिरोध बदलने पर शक्ति स्थिर मान लेना।
विस्तृत हल (मूल भाषा में)
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.
એક DC પરિપથમાં 20 V સપ્લાય સાથે 10 Ω નો અવરોધક જોડેલ છે.
કરંટ અને પાવરના સંદર્ભમાં નીચેના વિધાનો ધ્યાનમાં લો:
1. અવરોધકમાંથી વહેતો કરંટ 2 A છે.
2. અવરોધકમાં વપરાતો પાવર 40 W છે.
3. અવરોધ બમણો કરતાં કરંટ 1 A થાય છે.
4. અવરોધ બમણો કરતાં પાવર બદલાતો નથી.
ઉપરોક્તમાંથી કયું/કયા વિધાન સાચું/સાચા છે?
જવાબ અને પગલાવાર ઉકેલ
V=20 V, R=10 Ω: I=V/R=2 A અને P=VI=40 W. સમાન 20 V પર R ને 20 Ω કરતાં I=1 A અને P=20 W થાય છે. મુખ્ય સંબંધ: P=VI=I²R=V²/R.
પરીક્ષા મુદ્દો: અચળ V પર પાવર R ના વ્યસ્ત પ્રમાણમાં હોય છે. સામાન્ય ભૂલ: અવરોધ બદલાય ત્યારે પાવર અચળ માની લેવો.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
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.
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