Calculate equivalent resistance in series
Scenario
Traffic ek single road par move kar raha hai. Agar us raaste par `3` toll booths laga diye jayein, toh kya hoga?
Gaadiyon ko teeno toll booths cross karne hi padenge. Waise hi series circuit mein current ke paas ek hi rasta hota hai.
Mental model
Series circuit ek single highway ki tarah hai. Saare resistors ek ke baad ek chain mein lage hote hain.
Kyunki current ko kahin aur mudne ka raasta nahi milta, sabhi resistors se ek jaisa current gujarta hai. Par har resistor toll booth ki tarah total voltage (battery ki energy) ka kuch hissa khaa leta hai.
Explanation
Jab do ya do se zyada resistors end-to-end connect hote hain, toh unhe series mein kaha jata hai. Series circuit ki sabse khaas baat yeh hai ki pure circuit mein current (`I`) same rehta hai.
Lekin potential difference (Voltage) har resistor ke across bat (divide ho) jata hai. Agar battery ka voltage `V` hai, toh:
V = V_1 + V_2 + V_3
Ohm's law (`V = I R`) apply karne par:
I R_s = I R_1 + I R_2 + I R_3
`I` common nikal kar cancel ho jata hai, jisse equivalent resistance ka formula banta hai:
R_s = R_1 + R_2 + R_3
Iska matlab hai ki series mein lagaye gaye resistors ka total sum humesha kisi bhi individual resistor se bada hota hai. Isliye series combination use karne se circuit ka overall current decrease ho jata hai.
Worked example
Problem: Draw a schematic diagram of a circuit consisting of a battery of three cells of `2 V` each, a `5 Ω` resistor, an `8 Ω` resistor, and a `12 Ω` resistor, and a plug key, all connected in series. Find total resistance.
- Resistors series mein hain, isliye seedhe jodte hain.
- Values substitute karte hain.
- Total sum nikalte hain.
Answer: `25 Ω`
Problem: An electric lamp, whose resistance is `20 Ω`, and a conductor of `4 Ω` resistance are connected to a `6 V` battery in series. Calculate the total resistance of the circuit and current through the circuit.
- Dono resistances ko add karke total `R_s` nikalte hain.
- Battery ki voltage (`V`) di gayi hai.
- Circuit ka total current nikalne ke liye Ohm's law `I = V / R_s` use karte hain.
Answer: Total Resistance = `24 Ω`, Current = `0.25 A`
Key points
- Constant Current: The current remains the same through all components in a series circuit.
- Voltage Adds Up: The total voltage is the sum of voltages across each resistor (`V = V_1 + V_2 + V_3`).
- Equivalent Resistance Formula: `R_s = R_1 + R_2 + R_3`
Common mistakes
- Thinking current drops across resistors: Log sochte hain ki current series mein 'use up' ho jata hai. Asal mein current sabhi points par bilkul same rehta hai.
Recall questions
- In a series circuit, what physical quantity remains constant across all resistors?
- What is the equivalent resistance of `2 Ω` and `4 Ω` in series?
- What remains constant through all resistors in a series circuit?
Questions & answers
Draw a schematic diagram of a circuit consisting of a battery of three cells of `2 V` each, a `5 Ω` resistor, an `8 Ω` resistor, and a `12 Ω` resistor, and a plug key, all connected in series.
Total battery voltage = `6 V`. All components are in one closed loop.
Approach: Sum the cells for the battery voltage, place elements sequentially.
Three resistors of `2 Ω`, `3 Ω`, and `5 Ω` are in series. Find the total resistance.
`10 Ω`
Approach: `R_s = 2 + 3 + 5 = 10 Ω`.
Continue learning
Previous: Apply Ohm's law to circuits