Electricity – Resistance in Series & Parallel
Class 10 Science ke Electricity chapter me resistors in series and parallel ek bahut important topic hai. Board exams me is topic se direct numerical questions, conceptual questions, circuit-based questions aur competency-based questions pooche ja sakte hain.
Jab ek circuit me multiple resistors connected hote hain, to hum unki jagah ek single resistor consider kar sakte hain jo poori combination ke same electrical effect ko represent karta hai. Is resistance ko Equivalent Resistance ya Req kehte hain.
Equivalent Resistance → Same effect as the complete combination
Resistors ko mainly do ways me connect kiya ja sakta hai:
- Series Combination
- Parallel Combination
In dono combinations me current, voltage aur equivalent resistance ka behaviour alag hota hai. Isliye board exam ke liye inke basic rules ko clearly samajhna bahut important hai.
Resistance Kya Hai?
Resistance kisi conductor ya resistor ka electric current ke flow ko oppose karne ka property hai.
Resistance ka SI unit Ohm (Ω) hai.
Ohm's Law ke according:
V = IR
Therefore:
I = V/R
R = V/I
Agar circuit me multiple resistors hain, to total resistance calculate karne ke liye unki connection type identify karni hoti hai.
Series Combination of Resistors
Jab resistors ko one after another ek single path me connect kiya jata hai, to unhe series combination kehte hain.
Battery ── R₁ ── R₂ ── R₃ ── Battery
Series circuit me current ke liye sirf one path available hota hai.
Isliye series combination ka most important rule hai:
Same Current flows through every resistor.
Therefore:
I = I₁ = I₂ = I₃
Equivalent Resistance in Series
Series combination me equivalent resistance simply sabhi resistances ka sum hota hai.
Rs = R₁ + R₂ + R₃ + ...
For two resistors:
Rs = R₁ + R₂
Example
Suppose:
R₁ = 2 Ω
R₂ = 3 Ω
R₃ = 5 Ω
Then:
Rs = 2 + 3 + 5
Rs = 10 Ω
Isliye series combination ka equivalent resistance 10 Ω hoga.
Series Combination – Important Properties
1. Current Same Hota Hai
Series circuit me current ke liye sirf ek path hota hai.
Therefore:
I₁ = I₂ = I₃
2. Voltage Divide Hota Hai
Series circuit me total voltage individual resistors ke across divide hota hai.
V = V₁ + V₂ + V₃
3. Resistance Add Hota Hai
Rs = R₁ + R₂ + R₃
Therefore, series equivalent resistance kisi bhi individual resistance se greater hota hai.
Series Voltage Division
Ohm's Law ke according:
V₁ = IR₁
V₂ = IR₂
Since series combination me current same hota hai:
V₁/V₂ = R₁/R₂
Iska matlab hai ki jis resistor ka resistance greater hoga, uske across voltage drop bhi greater hoga.
Greater Resistance → Greater Voltage Drop
Series Example
Three resistors of 4 Ω, 6 Ω and 10 Ω are connected in series.
Equivalent resistance:
Rs = 4 + 6 + 10
Rs = 20 Ω
Therefore, the equivalent resistance is 20 Ω.
Parallel Combination of Resistors
Jab multiple resistors ko same two points ke across connect kiya jata hai, to unhe parallel combination kehte hain.
┌── R₁ ──┐
───────┤ ├───────
├── R₂ ──┤
└── R₃ ──┘
Parallel circuit me current ke liye multiple paths available hote hain.
Isliye current branches me divide hota hai.
Parallel Combination – Important Properties
1. Voltage Same Hota Hai
Parallel combination me har branch same two points ke across connected hoti hai.
Therefore:
V = V₁ = V₂ = V₃
2. Current Divide Hota Hai
Total current individual branch currents ka sum hota hai.
I = I₁ + I₂ + I₃
3. Equivalent Resistance Decrease Hota Hai
Parallel combination ka equivalent resistance smallest individual resistance se bhi less hota hai.
Equivalent Resistance in Parallel
For multiple resistors:
1/Rp = 1/R₁ + 1/R₂ + 1/R₃ + ...
For two resistors:
Rp = (R₁ × R₂)/(R₁ + R₂)
Is shortcut ko Product by Sum bhi yaad rakha ja sakta hai.
Parallel Example 1
Suppose:
R₁ = 6 Ω
R₂ = 3 Ω
Then:
Rp = (6 × 3)/(6 + 3)
Rp = 18/9
Rp = 2 Ω
Notice:
2 Ω < 3 Ω < 6 Ω ✅
Ye parallel equivalent resistance ka important check hai.
Equal Resistors in Parallel
Agar n identical resistors hain aur har resistor ki resistance R hai, to parallel equivalent resistance:
Rp = R/n
Example
Five resistors each have resistance 10 Ω and are connected in parallel.
Rp = 10/5
Rp = 2 Ω
n Equal Resistors – Series and Parallel
Agar n identical resistors hain aur har resistor ki resistance R hai, to formulas easily remember kiye ja sakte hain.
Series
Rs = nR
Example: 5 resistors of 2 Ω:
Rs = 5 × 2 = 10 Ω
Parallel
Rp = R/n
Example: 5 resistors of 10 Ω:
Rp = 10/5 = 2 Ω
Series vs Parallel – Complete Comparison
| Property | Series | Parallel |
|---|---|---|
| Current | Same | Divides |
| Voltage | Divides | Same |
| Paths | One | Multiple |
| Equivalent Resistance | Increases | Decreases |
| Formula | R₁ + R₂ + ... | 1/R₁ + 1/R₂ + ... |
| Equal Resistors | nR | R/n |
| Typical Household Wiring | No | Yes |
Most Important Shortcut
Series
Add Directly
Rs = R₁ + R₂ + R₃
Parallel – Two Resistors
Product / Sum
Rp = R₁R₂/(R₁ + R₂)
Equal Resistors Trick
Suppose 3 resistors each have resistance 6 Ω.
Series
Rs = 3 × 6 = 18 Ω
Parallel
Rp = 6/3 = 2 Ω
So:
Series → 18 Ω
Parallel → 2 Ω
Why Are Household Circuits Connected in Parallel?
Household electrical appliances are connected in parallel rather than series.
Iske important reasons hain:
- ✔ Each appliance receives the same supply voltage.
- ✔ Appliances can be operated independently.
- ✔ One appliance fail hone par other appliances normally continue kar sakte hain.
- ✔ Different appliances apni required current draw kar sakte hain.
Board Exam Point → Household Wiring = Parallel
Current and Voltage in Parallel
Ek common mistake ye hai ki students parallel circuit me current ko same samajh lete hain.
Parallel me:
V₁ = V₂ = V₃
Lekin:
I₁ may not equal I₂ or I₃
Ohm's Law:
I = V/R
Since voltage same hai, smaller resistance wale branch me current greater hoga.
Example – Current Division in Parallel
Two resistors:
R₁ = 2 Ω
R₂ = 4 Ω
They are connected in parallel across a 12 V source.
Current Through R₁
I₁ = V/R₁
I₁ = 12/2 = 6 A
Current Through R₂
I₂ = V/R₂
I₂ = 12/4 = 3 A
Therefore:
I₁ ≠ I₂
But:
V₁ = V₂ = 12 V
Notice that smaller resistance 2 Ω carries greater current.
Combination Circuits
Board exam me aise circuits bhi mil sakte hain jisme kuch resistors series me aur kuch parallel me connected hote hain. Aise circuit ko combination circuit kehte hain.
In circuits ko solve karne ke liye poore circuit ko ek hi step me solve karne ki zarurat nahi hoti.
Step-by-step equivalent resistance find karo.
Combination Circuit Solve Karne Ka Strategy
Step 1 → Identify obvious series or parallel pair
↓
Step 2 → Calculate equivalent resistance
↓
Step 3 → Replace that group with one resistor
↓
Step 4 → Repeat
↓
Step 5 → Find final Req
Combination Circuit Example
Suppose two resistors of 2 Ω each are connected in parallel, and their equivalent combination is connected in series with a 3 Ω resistor.
┌── 2Ω ──┐
───────┤ ├──── 3Ω ────
└── 2Ω ──┘
Step 1 – Parallel Pair
Rp = (2 × 2)/(2 + 2)
Rp = 4/4 = 1 Ω
Step 2 – Series Combination
Now 1 Ω is connected in series with 3 Ω.
Req = 1 + 3
Req = 4 Ω
Therefore, final equivalent resistance is 4 Ω.
Important Formula Box
Series
Rs = R₁ + R₂ + R₃
Parallel
1/Rp = 1/R₁ + 1/R₂ + 1/R₃
Two Parallel Resistors
Rp = R₁R₂/(R₁ + R₂)
Equal Resistors in Series
Rs = nR
Equal Resistors in Parallel
Rp = R/n
Ohm's Law
V = IR
I = V/R
R = V/I
Board Exam Question – Series and Parallel
Question: Two resistors of 4 Ω and 6 Ω are connected first in series and then in parallel. Find the equivalent resistance in both cases.
Part A – Series
Rs = R₁ + R₂
Rs = 4 + 6
Rs = 10 Ω
Part B – Parallel
Rp = (R₁R₂)/(R₁ + R₂)
Rp = (4 × 6)/(4 + 6)
Rp = 24/10
Rp = 2.4 Ω
Final Answer → Series = 10 Ω, Parallel = 2.4 Ω
Board Question – Concept
Question: Why are household electrical appliances connected in parallel?
Answer:
- Each appliance receives the same potential difference.
- Appliances can be operated independently.
- If one appliance stops working, the other branches can continue operating.
- Each appliance can draw current according to its resistance and power requirement.
Competency-Based Question
Two identical resistors each have resistance 10 Ω.
1. Find Series Resistance
Rs = 10 + 10
Rs = 20 Ω
2. Find Parallel Resistance
For two equal resistors:
Rp = R/2
Rp = 10/2 = 5 Ω
Comparison
Series → 20 Ω
Parallel → 5 Ω
Therefore:
Series increases equivalent resistance.
Parallel decreases equivalent resistance.
How to Identify Series and Parallel?
Circuit diagrams me sirf resistors ki physical position dekhkar decision nahi lena chahiye. Connection points ko carefully observe karo.
Series Identify Karne Ka Rule
Agar resistors ke beech current ke liye single path hai aur junction par current split nahi hota, to resistors series me hain.
Series → One Path → Same Current
Parallel Identify Karne Ka Rule
Agar do resistors same two junction points ke across connected hain, to wo parallel combination me hain.
Parallel → Same Two Points → Same Voltage
Common Mistakes
- ❌ Parallel resistors ke liye series formula use karna.
- ❌ Three or more parallel resistors ke liye blindly product/sum formula use karna.
- ❌ Parallel circuit me current same maan lena.
- ❌ Series circuit me voltage same maan lena.
- ❌ Equivalent resistance ki unit bhool jana.
- ❌ Circuit ke actual junction points identify na karna.
- ❌ Sirf physical closeness dekhkar resistors ko parallel maan lena.
- ❌ Combination circuit ko step-by-step simplify na karna.
Golden Rules
Series
Current Same
Voltage Divides
Resistance Adds
Parallel
Voltage Same
Current Divides
Resistance Decreases
5-Second Memory Trick
Series aur parallel ke two most important rules ko remember karne ke liye:
Series → Same Current
Parallel → Same Voltage
Yaad rakho:
S → I
P → V
Quick Revision Table
| Concept | Series | Parallel |
|---|---|---|
| Number of Paths | One | Multiple |
| Current | Same | Divides |
| Voltage | Divides | Same |
| Equivalent Resistance | R₁ + R₂ + ... | 1/R₁ + 1/R₂ + ... |
| Equal Resistors | nR | R/n |
| Resistance Compared With Smallest R | Greater | Smaller |
| Household Wiring | Not used as the standard arrangement | Used |
Important Board Exam Points
- ✔ Series combination has only one path for current.
- ✔ Current is same through all resistors in series.
- ✔ Voltage divides in series.
- ✔ Series equivalent resistance is the sum of individual resistances.
- ✔ Parallel combination provides multiple paths for current.
- ✔ Voltage is same across parallel branches.
- ✔ Total current is the sum of branch currents.
- ✔ Parallel equivalent resistance is less than the smallest individual resistance.
- ✔ For two parallel resistors, use Product/Sum.
- ✔ Equal resistors in series → nR.
- ✔ Equal resistors in parallel → R/n.
- ✔ Household circuits are connected in parallel.
- ✔ Smaller resistance in a parallel branch carries greater current for the same voltage.
Frequently Asked Questions (FAQs)
What happens to current in a series circuit?
Series circuit me current ke liye only one path hota hai, isliye current every resistor ke through same hota hai.
I₁ = I₂ = I₃
What happens to voltage in a series circuit?
Series circuit me total voltage individual resistors ke across divide hota hai.
V = V₁ + V₂ + V₃
What happens to voltage in a parallel circuit?
Parallel combination me every branch ke across potential difference same hota hai.
V = V₁ = V₂ = V₃
What happens to current in a parallel circuit?
Parallel circuit me current different branches me divide hota hai. Total current branch currents ka sum hota hai.
I = I₁ + I₂ + I₃
Which has greater equivalent resistance: series or parallel?
Same set of resistors ke liye series combination ka equivalent resistance parallel combination se greater hota hai.
Why is parallel equivalent resistance less than the smallest resistor?
Parallel combination me current ke liye multiple paths available hote hain. Is wajah se total opposition to current reduce hoti hai aur equivalent resistance smallest individual resistance se bhi less hota hai.
What is the formula for two resistors in parallel?
Rp = (R₁ × R₂)/(R₁ + R₂)
What is the formula for n equal resistors in parallel?
Agar n equal resistors hain aur each resistance R hai:
Rp = R/n
Why are household appliances connected in parallel?
Because each appliance gets the same supply voltage, appliances can operate independently, and failure of one appliance does not normally stop the other parallel branches.
PDF Notes
Electricity – Resistance in Series & Parallel ke detailed revision notes ko PDF format me directly yahan read kar sakte hain:
Final Thoughts
Resistance in Series and Parallel ko master karne ke liye sabse pehle current, voltage aur equivalent resistance ke behaviour ko samajhna zaruri hai. Sirf formulas yaad karne ke bajay circuit ka actual connection observe karo.
Series combination me one path hota hai, isliye current same hota hai. Voltage resistors ke across divide hota hai aur resistances directly add hoti hain:
Rs = R₁ + R₂ + R₃ + ...
Parallel combination me multiple paths hote hain, isliye current divide hota hai. Har branch ke across voltage same hota hai aur equivalent resistance reduce hoti hai:
1/Rp = 1/R₁ + 1/R₂ + 1/R₃ + ...
Do resistors ke liye shortcut yaad rakho:
Parallel → Product / Sum
Rp = R₁R₂/(R₁ + R₂)
Equal resistors ke case me calculation aur easy ho jati hai. n equal resistors of resistance R ke liye series me nR aur parallel me R/n hota hai.
Board exam ke liye sabse important memory trick hai:
S → I → Series means Same Current
P → V → Parallel means Same Voltage
Combination circuits me pehle obvious series ya parallel group identify karo, uska equivalent resistance calculate karo, us group ko single resistor se replace karo aur process repeat karo.
Finally, household wiring ka important concept yaad rakho: household appliances are connected in parallel because each appliance gets the required supply voltage and can operate independently.
Master Revision:
Series → One Path → Same Current → Voltage Divides → Resistance Adds
Parallel → Multiple Paths → Voltage Same → Current Divides → Resistance Decreases