🔢 Electricity Numericals

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Current I = Q/t
Ohm's Law V = IR
Resistance R = ρl/A
Power P = VI
Heating H = I²Rt
Energy E = Pt
🎯 Difficulty

20 TOTAL
4 EASY
8 HARD + VERY HARD
4 EXPERT
Numerical 1 – Current
EASY
Electric Current
A charge of 20 C passes through a conductor in 5 s. Calculate the current.
आसान भाषा में: 5 seconds में 20 coulomb charge flow हुआ है। Charge को time से divide करके current मिलेगा।
✅ Solution
Given: Q = 20 C, t = 5 s
Formula: I = Q/t
I = 20/5
I = 4 A
Answer: 4 A
Numerical 2 – Ohm's Law
EASY
Ohm's Law
A resistor of 5 Ω is connected to a 10 V source. Find the current flowing through it.
Voltage और resistance दी हुई है। V = IR से current निकालना है।
✅ Solution
V = 10 V
R = 5 Ω
I = V/R
I = 10/5 = 2 A
Answer: 2 A
Numerical 3 – Potential Difference
EASY
Potential Difference
A current of 3 A flows through a resistor of 4 Ω. Calculate the potential difference.
Current और resistance दी गई है। V = IR लगाएँगे।
✅ Solution
I = 3 A
R = 4 Ω
V = IR = 3 × 4
V = 12 V
Answer: 12 V
Numerical 4 – Series Resistance
EASY
Series Combination
Three resistors of 2 Ω, 3 Ω and 5 Ω are connected in series. Find the equivalent resistance.
Series में सभी resistances सीधे add होती हैं।
✅ Solution
R = R₁ + R₂ + R₃
R = 2 + 3 + 5
R = 10 Ω
Answer: 10 Ω
Numerical 5 – Parallel Resistance
MODERATE
Parallel Combination
Two resistors of 6 Ω and 3 Ω are connected in parallel. Find the equivalent resistance.
Parallel में reciprocal formula लगती है। दो resistors के लिए product/sum shortcut भी use कर सकते हैं।
✅ Solution
R = (R₁R₂)/(R₁ + R₂)
R = (6 × 3)/(6 + 3)
R = 18/9
R = 2 Ω
Answer: 2 Ω
Numerical 6 – Power
MODERATE
Electric Power
An appliance operates at 220 V and draws a current of 2 A. Calculate its power.
Power के लिए P = VI formula लगाएंगे।
✅ Solution
P = VI
P = 220 × 2
P = 440 W
Answer: 440 W
Numerical 7 – Electrical Energy
MODERATE
Electrical Energy
A 1000 W heater operates for 2 hours. Calculate the electrical energy consumed in kWh.
1000 W = 1 kW। Energy = Power × Time.
✅ Solution
P = 1000 W = 1 kW
t = 2 h
E = Pt
E = 1 × 2 = 2 kWh
Answer: 2 kWh
Numerical 8 – Resistance from Power
MODERATE
Power + Resistance
A 100 W appliance operates at 200 V. Find its resistance.
Power और voltage दी हुई है। P = V²/R से resistance निकालना आसान रहेगा।
✅ Solution
P = V²/R
R = V²/P
R = 200²/100
R = 400 Ω
Answer: 400 Ω
Numerical 9 – Resistance and Length
HARD
Resistance
A wire has resistance 5 Ω. If its length is doubled while keeping the material and area of cross-section unchanged, what will be the new resistance?
R = ρl/A में resistance length के directly proportional है। Length double होगी तो resistance भी double होगा।
✅ Solution
R ∝ l
Length doubled
New R = 2 × 5
Answer: 10 Ω
Numerical 10 – Area and Resistance
HARD
Resistance
A wire has resistance 12 Ω. If its cross-sectional area is doubled while length and material remain unchanged, find the new resistance.
R ∝ 1/A। Area double होने पर resistance half हो जाएगा।
✅ Solution
R₂ = R₁/2
R₂ = 12/2
Answer: 6 Ω
Numerical 11 – Heating Effect
HARD
Joule's Heating
A current of 2 A flows through a 5 Ω resistor for 10 s. Calculate the heat produced.
H = I²Rt formula use करेंगे।
✅ Solution
I = 2 A, R = 5 Ω, t = 10 s
H = I²Rt
H = 2² × 5 × 10
H = 200 J
Answer: 200 J
Numerical 12 – Power from Current
HARD
Power
A resistor of 10 Ω carries a current of 3 A. Calculate the power dissipated in the resistor.
P = I²R formula use करेंगे क्योंकि current और resistance दोनों दी गई हैं।
✅ Solution
P = I²R
P = 3² × 10
P = 90 W
Answer: 90 W
Numerical 13 – Series Circuit Current
VERY HARD
Series Circuit
Three resistors of 4 Ω, 6 Ω and 10 Ω are connected in series across a 40 V battery. Find the current in the circuit.
पहले series में total resistance निकालें। उसके बाद I = V/R से current निकालें।
✅ Solution
R = 4 + 6 + 10 = 20 Ω
I = V/R
I = 40/20
I = 2 A
Answer: 2 A
Numerical 14 – Parallel Current
VERY HARD
Parallel Circuit
Two resistors of 6 Ω and 3 Ω are connected in parallel across a 12 V battery. Find the total current drawn.
पहले equivalent resistance निकालें। फिर total current = V/Rp।
✅ Solution
Rp = (6 × 3)/(6 + 3)
Rp = 18/9 = 2 Ω
I = V/R
I = 12/2 = 6 A
Answer: 6 A
Numerical 15 – Electrical Energy in Joules
VERY HARD
Electrical Energy
A 500 W appliance operates continuously for 30 minutes. Calculate the electrical energy consumed in joules.
Power watt में है, इसलिए time seconds में convert करें। फिर E = Pt लगाएँ।
✅ Solution
P = 500 W
t = 30 × 60 = 1800 s
E = Pt
E = 500 × 1800
Answer: 900000 J = 9 × 10⁵ J
Numerical 16 – Power and Resistance
VERY HARD
Power + Resistance
An electrical appliance consumes 1000 W at 250 V. Find the current and resistance of the appliance.
पहले P = VI से current निकालें। उसके बाद R = V/I से resistance निकालें।
✅ Solution
I = P/V = 1000/250 = 4 A
R = V/I
R = 250/4 = 62.5 Ω
Answer: I = 4 A, R = 62.5 Ω
Numerical 17 – Resistivity
EXPERT
Resistivity
A wire has length 2 m and cross-sectional area 1 × 10⁻⁶ m². Its resistance is 4 Ω. Calculate its resistivity.
R = ρl/A formula में values डालकर ρ निकालना है। Area की scientific notation को carefully use करें।
✅ Solution
R = ρl/A
ρ = RA/l
ρ = (4 × 1 × 10⁻⁶)/2
ρ = 2 × 10⁻⁶ Ω m
Answer: 2 × 10⁻⁶ Ω m
Numerical 18 – Mixed Series Parallel
EXPERT
Mixed Circuit
A 4 Ω and 8 Ω resistor are connected in parallel. This combination is connected in series with a 3 Ω resistor. Find the total resistance.
पहले 4 Ω और 8 Ω का parallel equivalent निकालें। फिर उसमें 3 Ω series resistance add करें।
✅ Solution
Rp = (4 × 8)/(4 + 8)
Rp = 32/12 = 8/3 Ω
Rtotal = 3 + 8/3
Rtotal = 17/3 Ω
Answer: 17/3 Ω ≈ 5.67 Ω
Numerical 19 – Household Energy
EXPERT
Electrical Energy
A 2 kW heater is used for 3 hours daily for 5 days. Calculate the total electrical energy consumed in kWh.
पहले daily energy निकालें: P × time. फिर 5 days से multiply करें।
✅ Solution
P = 2 kW
Daily time = 3 h
Daily energy = 2 × 3 = 6 kWh
For 5 days = 6 × 5
Answer: 30 kWh
Numerical 20 – Final Mixed Challenge
EXPERT
Current + Power + Energy
A 220 V appliance draws a current of 5 A and operates for 4 hours. Find (a) its power and (b) the electrical energy consumed in kWh.
पहले P = VI से power निकालेंगे। फिर power को kW में बदलकर E = Pt से 4 घंटे की energy निकालेंगे।
✅ Step-by-Step Solution
V = 220 V, I = 5 A
P = VI
P = 220 × 5 = 1100 W
P = 1.1 kW
E = Pt
E = 1.1 × 4 = 4.4 kWh
Answer: P = 1100 W = 1.1 kW; Energy = 4.4 kWh
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