An RL circuit is excited by a DC step voltage. Then
1. Initial current through inductor is zero.
2. Final current depends only on resistance.
3. Time constant depends only on inductance.
4. Current rises exponentially with time.
Which of the above statements is/are correct?
Answer & step-by-step solution
In a first-order RL circuit driven by a DC step, inductor current cannot change instantaneously. The time constant depends on both inductance and resistance, so changing either alters the transient speed. Key relation: i(t)=V/R·(1−e^(−t/τ)); τ=L/R.
Exam focus: Initial inductor current is continuous; final DC inductor acts as a short circuit. Common trap: Do not write τ=L alone; resistance is part of the time constant.
Statement-wise Verification
- Statement 1 - Correct.
Initial current through inductor is zero.
Initial inductor current is continuous; final DC inductor acts as a short circuit. - Statement 2 - Correct.
Final current depends only on resistance.
Initial inductor current is continuous; final DC inductor acts as a short circuit. - Statement 3 - Incorrect.
Time constant depends only on inductance.
For a simple RL circuit τ=L/R, so resistance and inductance both matter - Statement 4 - Correct.
Current rises exponentially with time.
Starting from zero current, it rises exponentially toward the steady value V/R.
Core Concept
In a first-order RL circuit driven by a DC step, inductor current cannot change instantaneously. Starting from zero current, it rises exponentially toward the steady value V/R. The time constant depends on both inductance and resistance, so changing either alters the transient speed.
Formula / Key Relationship
i(t)=V/R·(1−e^(−t/τ)); τ=L/R.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 2. Option B is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 2, 4. Option D is incorrect because it includes incorrect statement(s) 3.
Exam Shortcut / Approach
Initial inductor current is continuous; final DC inductor acts as a short circuit.
Common Mistake
Do not write τ=L alone; resistance is part of the time constant.
Quick Revision
RL Step Response is linked with First-Order RL Circuit, Transient Analysis and Network Theory. Initial inductor current is continuous; final DC inductor acts as a short circuit.
एक RL परिपथ DC स्टेप वोल्टेज से उत्तेजित है। तब
1. प्रेरक से प्रारंभिक धारा शून्य है।
2. अंतिम धारा केवल प्रतिरोध पर निर्भर करती है।
3. समय स्थिरांक केवल प्रेरकत्व पर निर्भर करता है।
4. धारा समय के साथ घातांकीय रूप से बढ़ती है।
उपरोक्त में से कौन-सा/से कथन सही है/हैं?
उत्तर और चरणबद्ध हल
C — केवल 1, 2 और 4। प्रेरक धारा तुरंत नहीं बदलती (प्रारंभ में शून्य), i(t) = (V/R)(1 − e^(−t/τ)) घातांकीय रूप से बढ़ती है और अंतिम धारा V/R है। τ = L/R, इसलिए समय स्थिरांक L और R दोनों पर निर्भर है।
विस्तृत हल (मूल भाषा में)
Statement-wise Verification
- Statement 1 - Correct.
Initial current through inductor is zero.
Initial inductor current is continuous; final DC inductor acts as a short circuit. - Statement 2 - Correct.
Final current depends only on resistance.
Initial inductor current is continuous; final DC inductor acts as a short circuit. - Statement 3 - Incorrect.
Time constant depends only on inductance.
For a simple RL circuit τ=L/R, so resistance and inductance both matter - Statement 4 - Correct.
Current rises exponentially with time.
Starting from zero current, it rises exponentially toward the steady value V/R.
Core Concept
In a first-order RL circuit driven by a DC step, inductor current cannot change instantaneously. Starting from zero current, it rises exponentially toward the steady value V/R. The time constant depends on both inductance and resistance, so changing either alters the transient speed.
Formula / Key Relationship
i(t)=V/R·(1−e^(−t/τ)); τ=L/R.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 2. Option B is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 2, 4. Option D is incorrect because it includes incorrect statement(s) 3.
Exam Shortcut / Approach
Initial inductor current is continuous; final DC inductor acts as a short circuit.
Common Mistake
Do not write τ=L alone; resistance is part of the time constant.
Quick Revision
RL Step Response is linked with First-Order RL Circuit, Transient Analysis and Network Theory. Initial inductor current is continuous; final DC inductor acts as a short circuit.
એક RL પરિપથ DC સ્ટેપ વોલ્ટેજથી ઉત્તેજિત છે. તો
1. પ્રેરકમાંથી પ્રારંભિક પ્રવાહ શૂન્ય છે.
2. અંતિમ પ્રવાહ ફક્ત અવરોધ પર આધાર રાખે છે.
3. સમય અચળાંક ફક્ત પ્રેરકત્વ પર આધાર રાખે છે.
4. પ્રવાહ સમય સાથે ઘાતાંકીય રીતે વધે છે.
ઉપરોક્તમાંથી કયું/કયાં વિધાન સાચું/સાચાં છે?
જવાબ અને પગલાવાર ઉકેલ
C — ફક્ત 1, 2 અને 4. પ્રેરક પ્રવાહ તરત બદલાતો નથી (શરૂઆતમાં શૂન્ય), i(t) = (V/R)(1 − e^(−t/τ)) ઘાતાંકીય રીતે વધે છે અને અંતિમ પ્રવાહ V/R છે. τ = L/R, તેથી સમય અચળાંક L અને R બંને પર આધાર રાખે છે.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Statement-wise Verification
- Statement 1 - Correct.
Initial current through inductor is zero.
Initial inductor current is continuous; final DC inductor acts as a short circuit. - Statement 2 - Correct.
Final current depends only on resistance.
Initial inductor current is continuous; final DC inductor acts as a short circuit. - Statement 3 - Incorrect.
Time constant depends only on inductance.
For a simple RL circuit τ=L/R, so resistance and inductance both matter - Statement 4 - Correct.
Current rises exponentially with time.
Starting from zero current, it rises exponentially toward the steady value V/R.
Core Concept
In a first-order RL circuit driven by a DC step, inductor current cannot change instantaneously. Starting from zero current, it rises exponentially toward the steady value V/R. The time constant depends on both inductance and resistance, so changing either alters the transient speed.
Formula / Key Relationship
i(t)=V/R·(1−e^(−t/τ)); τ=L/R.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 2. Option B is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 2, 4. Option D is incorrect because it includes incorrect statement(s) 3.
Exam Shortcut / Approach
Initial inductor current is continuous; final DC inductor acts as a short circuit.
Common Mistake
Do not write τ=L alone; resistance is part of the time constant.
Quick Revision
RL Step Response is linked with First-Order RL Circuit, Transient Analysis and Network Theory. Initial inductor current is continuous; final DC inductor acts as a short circuit.
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