chapter 3 current electricity class 12




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CHAPTER 3 – CURRENT ELECTRICITY


Q 3.1 (English):
The storage battery of a car has an emf of 12 V. If the internal resistance of the battery is 0.4 Ω, what is the maximum current that can be drawn from the battery?

प्रश्न 3.1 (Hindi):
एक कार की बैटरी का विद्युत वाहक बल 12 V है। यदि बैटरी का आंतरिक प्रतिरोध 0.4 Ω है, तो उससे अधिकतम कितनी धारा ली जा सकती है?

Solution:

Given:
E = 12 V
r = 0.4 Ω

Formula:
Imax = E / r

I = 12 / 0.4
I = 30 A

Final Answer:
Maximum Current = 30 A
अधिकतम धारा = 30 A


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Q 3.2 (English):
A battery of emf 10 V and internal resistance 3 Ω is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery?

प्रश्न 3.2 (Hindi):
10 V विद्युत वाहक बल और 3 Ω आंतरिक प्रतिरोध वाली बैटरी एक प्रतिरोध से जुड़ी है। यदि धारा 0.5 A है, तो प्रतिरोध का मान ज्ञात करें। साथ ही टर्मिनल वोल्टेज ज्ञात करें।

Solution:

Given:
E = 10 V
r = 3 Ω
I = 0.5 A

Formula:
E = I(R + r)

10 = 0.5(R + 3)
10 = 0.5R + 1.5
0.5R = 8.5
R = 17 Ω

Terminal Voltage:
V = IR
V = 0.5 × 17
V = 8.5 V

Final Answer:
Resistance = 17 Ω
Terminal Voltage = 8.5 V

प्रतिरोध = 17 Ω
टर्मिनल वोल्टेज = 8.5 V


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Q 3.3 (English):
At room temperature (27°C) the resistance of a heating element is 100 Ω. What is its temperature if resistance becomes 117 Ω? Temperature coefficient is 1.70 × 10⁻⁴ °C⁻¹.

प्रश्न 3.3 (Hindi):
27°C पर हीटिंग एलिमेंट का प्रतिरोध 100 Ω है। यदि प्रतिरोध 117 Ω हो जाए, तो ताप ज्ञात करें। ताप गुणांक 1.70 × 10⁻⁴ °C⁻¹ है।

Solution:

Given:
R1 = 100 Ω
R2 = 117 Ω
T1 = 27°C
α = 1.70 × 10⁻⁴

Formula:
R2 = R1[1 + α(T2 - T1)]

117 = 100[1 + 1.70×10⁻⁴(T - 27)]

1.17 = 1 + 1.70×10⁻⁴(T - 27)

0.17 = 1.70×10⁻⁴(T - 27)

T - 27 = 1000

T = 1027°C

Final Answer:
Temperature = 1027°C
ताप = 1027°C


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Q 3.4 (English):
A small current is passed through a wire of length 15 m and area 6.0 × 10⁻⁷ m². Its resistance is 5 Ω. Find resistivity.

प्रश्न 3.4 (Hindi):
15 m लंबाई और 6.0 × 10⁻⁷ m² क्षेत्रफल वाले तार का प्रतिरोध 5 Ω है। प्रतिरोधकता ज्ञात करें।

Solution:

Formula:
ρ = RA / L

ρ = (5 × 6×10⁻⁷) / 15
ρ = 2 × 10⁻⁷ Ωm

Final Answer:
Resistivity = 2 × 10⁻⁷ Ωm
प्रतिरोधकता = 2 × 10⁻⁷ Ωm


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Q 3.5 (English):
Silver wire has resistance 2.1 Ω at 27.5°C and 2.7 Ω at 100°C. Find temperature coefficient.

प्रश्न 3.5 (Hindi):
चाँदी के तार का प्रतिरोध 27.5°C पर 2.1 Ω और 100°C पर 2.7 Ω है। ताप गुणांक ज्ञात करें।

Solution:

R2 = R1[1 + α(T2 - T1)]

2.7 = 2.1[1 + α(72.5)]

2.7/2.1 = 1 + 72.5α

1.2857 - 1 = 72.5α

α = 0.00394 °C⁻¹

Final Answer:
α = 3.94 × 10⁻³ °C⁻¹


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Q 3.6 (English):
Nichrome heater draws 3.2 A initially and 2.8 A steady from 230 V. Find steady temperature.

प्रश्न 3.6 (Hindi):
निक्रोम हीटर 230 V से प्रारंभ में 3.2 A और स्थिर अवस्था में 2.8 A धारा लेता है। स्थिर ताप ज्ञात करें।

Solution:

R1 = 230 / 3.2 = 71.88 Ω
R2 = 230 / 2.8 = 82.14 Ω

82.14 = 71.88[1 + 1.7×10⁻⁴(T - 27)]

Solving:
T ≈ 847°C

Final Answer:
Temperature ≈ 847°C
ताप ≈ 847°C


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Q 3.7 (English):
Determine the current in each branch of the network shown in Fig 3.20.

प्रश्न 3.7 (Hindi):
चित्र 3.20 में दर्शाए गए परिपथ की प्रत्येक शाखा में धारा ज्ञात करें।

Final Answer:
I1 = 2.5 A
I2 = 0.625 A
I3 = 0.875 A


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Q 3.8 (English):
Battery 8 V, internal resistance 0.5 Ω, charged by 120 V supply using 15.5 Ω resistor. Find terminal voltage.

प्रश्न 3.8 (Hindi):
8 V और 0.5 Ω आंतरिक प्रतिरोध वाली बैटरी को 120 V सप्लाई से 15.5 Ω प्रतिरोध के माध्यम से चार्ज किया जा रहा है। टर्मिनल वोल्टेज ज्ञात करें।

Solution:

Total Resistance = 16 Ω
Net Voltage = 120 - 8 = 112 V

I = 112 / 16 = 7 A

Terminal Voltage:
V = E + Ir
V = 8 + (7×0.5)
V = 11.5 V

Final Answer:
Terminal Voltage = 11.5 V
टर्मिनल वोल्टेज = 11.5 V


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Q 3.9 (English):
Number density 8.5×10²⁸ m⁻³, wire length 3 m, area 2×10⁻⁶ m², current 3 A. Find time for electron to drift.

प्रश्न 3.9 (Hindi):
इलेक्ट्रॉन संख्या घनत्व 8.5×10²⁸ m⁻³, तार की लंबाई 3 m, क्षेत्रफल 2×10⁻⁶ m², धारा 3 A है। इलेक्ट्रॉन को सिरे से सिरे तक जाने में कितना समय लगेगा?

Solution:

I = neAvd

vd = I / neA

vd ≈ 1.1×10⁻⁴ m/s

Time:
t = L / vd

t ≈ 7.5 hours

Final Answer:
Time ≈ 7.5 hours
समय ≈ 7.5 घंटे



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