Current Electricity — Maharashtra (SSC) Class 9 Science Solutions (Free)

Ohm's Law states that the current flowing through a conductor is directly proportional to the potential difference (voltage) applied across it, PROVIDED the temperature and other physical conditions of the conductor remain constant. Formula: V = IR (or equivalently I = V/R), where V is potential difference, I is current, and R is resistance. SI unit of resistance: the ohm (Ω), defined as 1 Ω = 1 volt / 1 ampere. The condition "temperature constant" matters because a conductor's resistance itself typically changes with temperature — Ohm's Law describes the relationship between V and I only while R stays fixed; it does NOT claim that R itself never changes under any circumstances, which is exactly why very hot filaments (like in an incandescent bulb) don't perfectly obey a simple straight-line V–I relationship.

Given: V = 12 V, R = 4 Ω Using Ohm's Law, I = V/R: I = 12/4 = 3 A The current flowing through the resistor is 3 amperes.

Electric current is the rate at which electric charge flows through a conductor — how much charge passes a given point per unit time. SI unit: the ampere (A), where 1 ampere = 1 coulomb of charge flowing per second. What 1 ampere physically means: if a wire carries a current of 1 A, exactly 1 coulomb of electric charge (equivalent to roughly 6.24 × 10¹⁸ electrons) passes through any given cross-section of that wire every single second. By convention, the direction of "conventional current" is defined as flowing from the positive terminal of a source to the negative terminal through the external circuit — even though the actual charge carriers in a metal wire (electrons) physically move in the OPPOSITE direction, from negative to positive. This convention was fixed before electrons were even discovered, and has simply been kept ever since for consistency.

For resistors connected in SERIES (one after another along a single path), the equivalent resistance is simply the SUM of the individual resistances, since the same current must pass through each one in turn, and each adds its own opposition: R_total = R₁ + R₂ + R₃ Given: R₁ = 2 Ω, R₂ = 3 Ω, R₃ = 5 Ω R_total = 2 + 3 + 5 = 10 Ω The equivalent resistance is 10 Ω. Note that a series combination's total resistance is always GREATER than any single resistor in it — adding more resistors in series always increases the total opposition to current flow.

Resistance is the opposition a conductor offers to the flow of electric current through it. Four factors affecting resistance: 1. Material of the conductor: different materials have different intrinsic resistivity (ρ) — for example, copper has much lower resistivity than nichrome, which is exactly why copper is used for ordinary wiring while nichrome (deliberately higher resistance) is used for heating elements. 2. Length of the conductor (L): resistance is directly proportional to length (R ∝ L) — a longer wire gives charge carriers a longer path to travel, encountering more collisions and opposition along the way. 3. Cross-sectional area (A): resistance is inversely proportional to cross-sectional area (R ∝ 1/A) — a thicker wire gives charge carriers more room to flow through simultaneously, similarly to how a wider pipe allows water to flow more easily than a narrow one. 4. Temperature: for most metallic conductors, resistance INCREASES as temperature rises, since hotter metal atoms vibrate more vigorously, causing more frequent collisions with the flowing charge carriers. These four factors combine in the resistivity formula: R = ρL/A, where ρ (resistivity) captures the material-dependent factor, and the other two variables — length and area — capture the conductor's specific physical shape.

For resistors connected in PARALLEL (providing multiple separate paths for current), the equivalent resistance is found from: 1/R_total = 1/R₁ + 1/R₂ Given: R₁ = 6 Ω, R₂ = 3 Ω 1/R_total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2 R_total = 2 Ω The equivalent resistance is 2 Ω. Notice that this result (2 Ω) is SMALLER than either individual resistor (6 Ω and 3 Ω) — a parallel combination always has a total resistance LESS than its smallest individual resistor, since adding more parallel paths always makes it easier overall for current to flow, the opposite effect of adding resistors in series.

An open circuit is one where the electrical path is broken or incomplete — for example, when a switch is turned OFF. Since there is no complete conducting path, no current flows, even though a potential difference (voltage) may still exist across the break, ready to drive current the moment the circuit is completed. A closed circuit is one where the electrical path is fully complete — for example, when a switch is turned ON. Current flows continuously around the complete loop as long as it remains closed and a source of potential difference is connected. A simple example makes the distinction concrete: a light bulb connected to a battery through a switch stays OFF when the switch is open (broken circuit, no current), and turns ON the instant the switch is closed (completed circuit, current begins flowing) — the potential difference from the battery was present the whole time in both cases, but current only flows once the physical path is unbroken.

Using the resistivity formula: R = ρL/A Given: ρ = 1.5 × 10⁻⁶ Ω·m, L = 2 m, A = 0.5 × 10⁻⁶ m² R = (1.5 × 10⁻⁶ × 2) / (0.5 × 10⁻⁶) R = (3 × 10⁻⁶) / (0.5 × 10⁻⁶) R = 6 Ω The resistance of the wire is 6 Ω. This formula is exactly how manufacturers calculate what length and thickness of a particular metal is needed to produce a wire or heating element with a specific target resistance.