Circuits — Set 4

Correct Answer: C. V = IR

• **V = IR** = Ohm's law: voltage across a conductor equals current times resistance at constant temperature. • **V = IR; R = V/I constant for ohmic conductors** — A V-I graph for an ohmic conductor is a straight line through the origin. • 💡 Wrong-option analysis: R = IV: product IV gives power P, not resistance; V = I/R: that means V decreases as R increases, rearranges incorrectly; I = VR: implies current increases with resistance, which is wrong.

Correct Answer: C. Ohm

• **Ohm** = Resistance is measured in ohm (Ω); by definition, 1 Ω = 1 V / 1 A. • **1 Ω = 1 V/A** — Named after Georg Simon Ohm; resistance measures opposition to current flow. • 💡 Wrong-option analysis: Ampere: SI unit of current; Watt: SI unit of power (= V×A); Volt: SI unit of electric potential difference.

Correct Answer: A. Junction rule

• **Junction rule** = KCL is called the junction rule because it applies at nodes (junctions) where currents branch. • **Junction rule: ΣI_in = ΣI_out at every node** — Based on conservation of charge; no charge accumulates at a junction in steady state. • 💡 Wrong-option analysis: Power rule: no standard circuit rule by this name; Loop rule: that is Kirchhoff's voltage law (KVL); Bridge rule: not a standard Kirchhoff terminology.

Correct Answer: B. Loop rule

• **Loop rule** = KVL is called the loop rule because it states that the algebraic sum of all voltages around any closed loop equals zero. • **Loop rule: ΣV = 0 around closed loop** — Based on conservation of energy; potential returns to its starting value after one complete loop. • 💡 Wrong-option analysis: Charge rule: not a standard Kirchhoff name; Resistance rule: no standard rule by this name; Junction rule: that is Kirchhoff's current law (KCL).

Correct Answer: C. Req = R1 + R2 + ...

• **R_eq = R₁ + R₂ + ...** = In series the same current flows through each resistor; total voltage drop sums up, giving R_eq = ΣRᵢ. • **Series: R_eq = R₁ + R₂ + ... (always greater than any single resistor)** — Adding more resistors in series always increases total resistance. • 💡 Wrong-option analysis: R_eq = R₁ − R₂: subtraction is never the series rule; R_eq = 1/R₁ + 1/R₂: that is 1/R_eq for parallel, not series; R_eq = R₁R₂/(R₁+R₂): that is the two-resistor parallel formula.

Correct Answer: A. 1/Req = 1/R1 + 1/R2 + ...

• **1/R_eq = 1/R₁ + 1/R₂ + ...** = In parallel, conductances add: G_eq = G₁ + G₂ +..., which is 1/R_eq = 1/R₁ + 1/R₂ +... • **Parallel: R_eq < any individual branch resistance** — Adding more parallel paths always reduces total resistance. • 💡 Wrong-option analysis: R_eq = R₁R₂: product without denominator has wrong units; R_eq = R₁ + R₂: that is the series rule; R_eq = R₁ − R₂: subtraction is never the parallel rule.

Correct Answer: D. P = I^2R

• **P = I²R** = Power dissipated in a resistor is P = I²R; combining with V = IR also gives P = V²/R = VI. • **P = I²R (watts when I in amperes, R in ohms)** — Doubling current quadruples power due to the I² term. • 💡 Wrong-option analysis: P = IR: has units of volts (V = IR), not watts; P = I/R: no standard power formula; P = R/I²: inverted form, gives Ω/A² not watts.

Correct Answer: B. E = VIt

• **E = VIt** = Energy = Power × time = VI × t = VIt, measured in joules. • **E = VIt; in kWh = VIt/3600000** — This is the basis for electricity billing; a 1 kW device running 1 hour uses 1 kWh. • 💡 Wrong-option analysis: E = V/I: that is resistance R by Ohm's law, not energy; E = VI/t: divides by time, giving power per second not energy; E = It/V: no standard energy formula.

Correct Answer: B. ρ

• **ρ** = Resistivity is denoted by the Greek letter rho (ρ); it is a material property in the formula R = ρL/A. • **R = ρL/A; ρ in Ω·m** — Its reciprocal is conductivity σ (sigma), so ρ × σ = 1. • 💡 Wrong-option analysis: R: symbol for resistance, not resistivity; σ: symbol for electrical conductivity (the reciprocal of ρ); G: symbol for conductance (= 1/R), not resistivity.

Correct Answer: B. Siemens

• **Siemens** = Conductance G = 1/R is measured in siemens (S); 1 S = 1 A/V = 1/Ω. • **1 S = 1 A/V** — Siemens replaced the older unit 'mho' (ohm spelled backward, symbol ℧). • 💡 Wrong-option analysis: Coulomb: unit of electric charge; Ohm: unit of resistance (inverse of siemens); Volt: unit of potential difference.