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Physics · CDS

PC08 — Current Electricity & Circuits

📖 PC08 · CDS General Science — Physics 🎯 CDS Level : High Priority

Electricity is the most practically relevant chapter in CDS Physics. Ohm's law, resistance combinations (series and parallel), and the heating effect of current appear in every few CDS papers. Household electricity concepts — units of energy, fuses, earthing — are also directly tested.

📌 CDS focuses on:
(1) Ohm's law V = IR — numerical problems;
(2) Series vs parallel resistance — calculating combined resistance;
(3) Joule's law of heating — which appliance heats more;
(4) Electrical power P = VI = I²R = V²/R;
(5) Electrical energy units (kWh); household electricity concepts;
(6) Why bulbs in parallel are brighter and independent of each other.

Topics at a Glance

① Electric Current & EMF

Charge, current, potential difference, EMF

② Ohm's Law & Resistance

V=IR; factors affecting R; resistivity

③ Series & Parallel Circuits

Combined resistance; voltage/current sharing

④ Heating Effect of Current

Joule's law; fuse; household heating

⑤ Electrical Power & Energy

P=VI; units kWh; electricity bill

⑥ Household Electricity

Fuse, earthing, AC/DC, safety

1. Electric Current, Potential & Ohm's Law

1.1

Current, Voltage, Resistance — The Fundamental Trio

Every circuit problem reduces to applying these three quantities and Ohm's Law

⚡ Definitions & Ohm's Law

Electric Current: I = Q / t [unit: Ampere (A)] Q = charge in Coulombs; t = time in seconds Potential Difference: V = W / Q [unit: Volt (V)] Work done per unit charge between two points Ohm's Law: V = I × R [R unit: Ohm (Ω)] At constant temperature, current is proportional to voltage. R = V/I (Resistance = Voltage / Current) Resistivity (ρ): R = ρ L / A L = length of conductor; A = cross-sectional area ρ depends only on material and temperature (not dimensions)

Ohm's law does NOT apply to all conductors — diodes, LEDs, and electrolytes are non-ohmic devices. Also, Ohm's law breaks down at very high temperatures.

📌 Factors Affecting Resistance

Increases with length: R ∝ L
Decreases with area: R ∝ 1/A
Depends on material (resistivity ρ)
Increases with temperature (metals)
Decreases with temperature (semiconductors, thermistors)

⚡ V–I Graph (Ohm's Law)

For an ohmic conductor: V–I graph is a straight line through origin
Slope = V/I = R (steeper slope = higher resistance)
Non-ohmic devices (diodes): curved V–I graph
Silver: lowest resistivity (best conductor)
Nichrome: high resistivity (used in heater coils)

2. Series & Parallel Resistance Circuits

2.1

Combining Resistors — Rules & Practical Meaning

Two fundamentally different ways to connect resistors — with opposite effects on total resistance

Fig. 1 — Series: all components share the same current; voltage is divided. Parallel: all components share the same voltage; current is divided. Removing one component in series breaks the whole circuit; in parallel it doesn't.

⚡ Series vs Parallel — Key Formulae

SERIES: R_total = R₁ + R₂ + R₃ + ... (total resistance INCREASES) Same current I through all: I₁ = I₂ = I₃ = I Voltage divides: V₁ + V₂ + V₃ = V_total PARALLEL: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ (total resistance DECREASES) Same voltage across all: V₁ = V₂ = V₃ = V Current divides: I₁ + I₂ + I₃ = I_total For just TWO resistors in parallel: R_total = R₁R₂ / (R₁ + R₂) ← product over sum formula

In homes, all appliances (bulbs, fans, ACs) are connected in parallel — each gets the same 230V supply and can be switched independently. If in series, switching off one would switch off all (like old Christmas tree lights).

3. Heating Effect of Current (Joule's Law)

3.1

How Current Produces Heat — and Practical Applications

The basis of electric heaters, fuses, incandescent bulbs, and more

⚡ Joule's Law of Heating & Power

Heat produced: H = I² R t [Joule's Law] H = heat (J); I = current (A); R = resistance (Ω); t = time (s) Electrical Power: P = V I = I²R = V²/R [unit: Watt (W)] P = VI (most general) P = I²R (useful when I and R are known) P = V²/R (useful when V and R are known) Electrical Energy: E = P × t = V I t [unit: Joule, or kWh] 1 kWh (kilowatt-hour) = 1 unit of electricity on your bill 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J Cost: Units consumed = (Power in kW) × (Time in hours) Example: 1000W heater for 5 hours = 5 kWh = 5 units

A 100W bulb in a parallel circuit draws MORE current (I = P/V = 100/230 ≈ 0.43A) than a 60W bulb (0.26A). Since P = V²/R, a 100W bulb has LOWER resistance than a 60W bulb (at 230V supply).

📏 Electric Fuse — Protection Device

A thin wire with low melting point (tin-lead alloy)
Placed in series with the circuit
Melts and breaks circuit when current exceeds safe limit
Protects appliances from overcurrent and short circuits
Must be placed on the live wire (not neutral)
Modern alternative: MCB (Miniature Circuit Breaker) — reusable

🔹 Earthing (Grounding)

Connects metal body of appliance to Earth (ground)
In case of fault (current leaks to body), current safely flows to earth
Prevents electric shock to users
Earth wire is typically green/yellow insulation
Live wire: red/brown; Neutral: black/blue

⚠ CDS Electricity Traps: (1) A 100W bulb has lower resistance than a 60W bulb when used on the same voltage (P = V²/R). (2) In a series circuit, more resistance means more voltage drop, NOT more current. (3) The unit of electrical energy consumed (kWh) is different from the unit of power (watt). (4) Fuse wire must always be on the live wire — never on the neutral.

📝 CDS PYQ

Current Electricity

Q1. Three resistors of 3 Ω each are connected in parallel. The combined resistance is:

(a) 9 Ω (b) 3 Ω (c) 1 Ω (d) 6 Ω

Answer: (c) 1 Ω
For n equal resistors R in parallel: R_total = R/n = 3/3 = 1 Ω. More formally: 1/R_total = 1/3 + 1/3 + 1/3 = 3/3 = 1, so R_total = 1 Ω. Note: parallel combination always gives resistance LESS than the smallest individual resistor — 1 Ω is less than 3 Ω. ✓

Q2. A heater of 1000 W is used for 2 hours daily. How many units (kWh) of electricity are consumed in 30 days?

(a) 30 units (b) 60 units (c) 6 units (d) 120 units

Answer: (b) 60 units
Units = Power (kW) × Time (h) × Days = 1 kW × 2 h × 30 = 60 kWh = 60 units. This is exactly how electricity bills are calculated. 1 unit = 1 kWh. If electricity costs ₹8/unit, this heater costs ₹480 per month.

Q3. Which of the following has the highest resistance — a 40W, 60W, or 100W bulb, all rated for the same voltage?

(a) 100 W (b) 60 W (c) 40 W (d) All have the same resistance

Answer: (c) 40 W bulb has the highest resistance
From P = V²/R, R = V²/P. At the same voltage V: R ∝ 1/P. So lower power → higher resistance. R_40W = V²/40; R_60W = V²/60; R_100W = V²/100. The 40W bulb has the HIGHEST resistance and the 100W bulb has the LOWEST resistance at the same supply voltage. This is a repeated CDS trap question.

Q4. In household wiring, all electrical appliances are connected in:

(a) Series (b) Parallel (c) Series-parallel combination (d) Neither series nor parallel

Answer: (b) Parallel
All household appliances are connected in parallel across the 230V AC supply. This ensures: (1) each appliance gets the full 230V supply; (2) each appliance can be switched on/off independently; (3) failure of one appliance doesn't affect others. If connected in series, all would have to operate simultaneously and switching off one would cut off all.

📚 Formula Sheet — PC08

⚡ Ohm's Law

V = IR; I = V/R; R = V/I
R = ρL/A (resistivity formula)
Ohmic: linear V-I graph
R increases with temp (metals)
R decreases with temp (semiconductors)

📌 Circuits

Series: R_T = R₁+R₂+... (increases)
Parallel: 1/R_T = 1/R₁+1/R₂+... (decreases)
Two parallel: R = R₁R₂/(R₁+R₂)
Series: same I; different V
Parallel: same V; different I

🔥 Power & Heating

P = VI = I²R = V²/R
H = I²Rt (Joule's law)
E = Pt (energy in joules)
1 kWh = 3.6 × 10⁶ J = 1 unit
Lower power → higher R (at same V)

📏 Safety & AC

Fuse: on live wire; melts on overload
Earthing: prevents electric shock
India AC: 230V, 50 Hz
Live: red/brown; Neutral: black/blue
Earth wire: green/yellow

⚡ Quick Revision Booster — PC08

⚡ Ohm's Law Tricks

V = IR; rearrange: I=V/R; R=V/I
V-I graph slope = resistance
R doubles if length doubles
R halves if area doubles
Metals: R increases with temp

📌 Series vs Parallel

Series: R adds up (increases total)
Parallel: R decreases (less than smallest)
Series: same I; parallel: same V
Home wiring: parallel
Two parallel: R₁R₂/(R₁+R₂)

🔥 Power Facts

P = VI = I²R = V²/R
At same V: higher W → lower R
Joule: H = I²Rt
1 kWh = 1 unit on bill
100W bulb: lower R than 40W bulb

📏 Fuse & Safety

Fuse on live wire (always)
Fuse melts → breaks circuit
MCB: modern reusable fuse
Earthing: safety against leakage
Short circuit: very high current

🚨 CDS Traps

Higher W → lower R (not higher!)
Fuse on live wire, not neutral
Parallel: each gets full voltage
Series: removing one breaks all
R parallel always less than smallest R

🔋 India AC Supply

220–230 V; 50 Hz frequency
AC (alternating current) in homes
DC (direct current): batteries
Transformer: steps up/down AC voltage
RMS voltage of AC = peak/√2

📝 Practice Exercise

Attempt independently before checking answers.

E-01

A 6V battery is connected to a 3Ω resistor. The current flowing is:

(a) 18 A
(b) 2 A
(c) 0.5 A
(d) 9 A

E-02

Two resistors of 4Ω and 6Ω are connected in parallel. The combined resistance is:

(a) 10 Ω
(b) 2.4 Ω
(c) 5 Ω
(d) 1 Ω

E-03

An electric iron of 1500 W is used for 2 hours. The electrical energy consumed in kWh is:

(a) 750 kWh
(b) 3 kWh
(c) 0.75 kWh
(d) 3000 kWh

E-04

The heating element of a heater is made of nichrome wire. This is because nichrome has:

(a) Low resistivity
(b) High resistivity and high melting point
(c) Low melting point
(d) Low conductivity

E-05

If the length of a wire is doubled and its cross-sectional area is halved, the resistance becomes:

(a) Same
(b) Doubled
(c) Halved
(d) Four times

Answers: E-01: (b) 2 A [I = V/R = 6/3 = 2 A] | E-02: (b) 2.4 Ω [R = R₁R₂/(R₁+R₂) = 4×6/(4+6) = 24/10 = 2.4 Ω] | E-03: (b) 3 kWh [E = P×t = 1.5 kW × 2 h = 3 kWh] | E-04: (b) High resistivity and high melting point — nichrome resists current flow (generates heat) and doesn't melt at high temperatures | E-05: (d) Four times [R = ρL/A; new R = ρ(2L)/(A/2) = 4ρL/A = 4R]

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