SATHEE: Shortcut Methods

JEE Main:

1. Total resistance in series circuit:
For resistors in series, add their resistances. $T o t a l R e s i s t a n c e = 10 Ω + 20 Ω = 30 Ω$

2. Total resistance in parallel circuit: For resistors in parallel, use the formula: $\frac{1}{R_{T o t a l}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} \frac{1}{R_{T o t a l}} = \frac{1}{10 Ω} + \frac{1}{20 Ω} + \frac{1}{30 Ω}$ $\frac{1}{R_{T o t a l}} = \frac{11}{60 Ω} R_{T o t a l} = 5.45 Ω$

3. Current in series circuit: Use Ohm’s Law: $I = \frac{V}{R}$ $I = \frac{12 V}{(10 Ω + 20 Ω)} = 0.4 A$

4. Current in parallel circuit: For each branch current $(I_{1} = \frac{V}{R_{1}}), (I_{2} = \frac{V}{R_{2}}), (I_{3} = \frac{V}{R_{3}})$ $I_{1} = \frac{12 V}{10 Ω} = 1.2 A$ $I_{2} = \frac{12 V}{20 Ω} = 0.6 A$ $I_{3} = \frac{12 V}{30 Ω} = 0.4 A$

5. Total resistance in series-parallel combination: Simplify the circuit by combining series or parallel parts first, then calculate total resistance.

CBSE Board Exams:

1. Total resistance in series circuit: $R_{T o t a l} = 10 Ω + 20 Ω + 30 Ω = 60 Ω$

2. Total resistance in parallel circuit: $\frac{1}{R_{T o t a l}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \frac{1}{R_{T o t a l}} = \frac{1}{10 Ω} + \frac{1}{20 Ω}$ $\frac{1}{R_{T o t a l}} = \frac{3}{20 Ω} R_{T o t a l} = \frac{20}{3} Ω$

3. Current in series circuit: Use Ohm’s Law: $I = \frac{V}{R}$ $I = \frac{9 V}{10 Ω + 20 Ω} = 0.3 A$

4. Current in parallel circuit: For each branch, $I = \frac{V}{R}$ $I_{1} = \frac{9 V}{10 Ω} = 0.9 A$ $I_{2} = \frac{9 V}{20 Ω} = 0.45 A$ $I_{3} = \frac{9 V}{30 Ω} = 0.3 A$

5. Total resistance in series-parallel combination: First, combine resistors in series or parallel and simplify the circuit, then calculate the total resistance.

Shortcut Methods

JEE Main:

CBSE Board Exams:

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

NCERT Exercise Video Solution

Shortcut Methods

JEE Main:

CBSE Board Exams:

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

NCERT Exercise Video Solution

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