Equivalent resistance of resistors in series and in parallel श्रेणी और समांतर क्रम में प्रतिरोधकों का तुल्य प्रतिरोध
Aim: To find the resistance of two resistors separately and then their equivalent resistance in series and in parallel, and to verify Rs = R₁ + R₂ and 1/Rp = 1/R₁ + 1/R₂.
Apparatus उपकरण
- Two resistors R₁ and R₂
- Battery eliminator or cells
- Ammeter (0–1 A, least count 0.01 A)
- Voltmeter (0–5 V, least count 0.05 V)
- Rheostat, plug key and connecting wires
Theory सिद्धांत
In series the same current flows through both resistors and the potential differences add, so the equivalent resistance is Rs = R₁ + R₂ (more than either). In parallel both resistors have the same potential difference and the currents add, so 1/Rp = 1/R₁ + 1/R₂ (less than the smaller one). Each resistance is found from Ohm’s law, R = V/I, using an ammeter in series and a voltmeter across the resistor or combination.
Procedure विधि
- Connect R₁ alone with the battery, key, ammeter and rheostat in series and the voltmeter across R₁. Take three readings of V and I and find R₁ = V/I.
- Repeat with R₂ alone.
- Connect R₁ and R₂ in series and the voltmeter across the combination. Take three readings and find Rs.
- Connect R₁ and R₂ in parallel and the voltmeter across the combination. Take three readings and find Rp.
- Compare the measured Rs and Rp with the values calculated from R₁ and R₂.
Simulated experiment अनुकरण प्रयोग
Your resistors are marked R₁ = 2 Ω and R₂ = 4 Ω (± 5%). Take three readings for each arrangement.
Observation table प्रेक्षण तालिका
| Arrangement | V (volt) | I (ampere) | R = V/I (Ω) | Remove |
|---|---|---|---|---|
| Record readings for R₁, R₂, series and parallel. | ||||
- R₁ (mean)
- —
- R₂ (mean)
- —
- Rs measured / R₁ + R₂
- — / —
- Rp measured / R₁R₂/(R₁+R₂)
- — / —
Record and fill readings for all four arrangements to check the laws.
Precautions सावधानियाँ
- Keep connections tight and clean.
- Join the voltmeter across exactly the combination being measured.
- Keep the current small and switch off between readings so the resistors do not heat up.
- Avoid parallax while reading the meters.
Sources of error त्रुटि के स्रोत
- Resistors have a tolerance (often ±5%), so they are not exactly their marked values.
- Resistance of connecting wires and contacts adds a little to the series value.
- Least count and parallax errors in the meters.
- Heating of resistors during the experiment.
Viva voce questions मौखिक प्रश्न
Q1. What is the equivalent resistance of 2 Ω and 3 Ω in series and in parallel?
Series: 5 Ω. Parallel: (2 × 3)/(2 + 3) = 1.2 Ω.
Q2. Which quantity is the same for all resistors in series? In parallel?
In series the current is the same; in parallel the potential difference is the same.
Q3. Why are household appliances connected in parallel?
Each appliance gets the full mains voltage, can be switched on or off independently, and a fault in one does not stop the others.
Q4. Is the parallel equivalent resistance more or less than each resistor?
Less than the smallest resistance in the combination.
Q5. What happens to the total current if one more resistor is added in parallel?
It increases, because the equivalent resistance decreases.