Electricity & Magnetism — Part 2: 40 MCQs with Explanations

Positron (e⁺) has same mass as electron but positive charge. Discovered by Anderson in cosmic rays (1932).

Ionizing power: α > β > γ. Alpha has large mass and charge, creates dense ionization along short path.

Inductive reactance X_L = ωL = 2πfL. Current lags voltage by 90°.

Capacitive reactance X_C = 1/ωC = 1/(2πfC). Current leads voltage by 90°.

Average power P_avg = V_rms I_rms cosφ, where φ = phase angle between voltage and current. cosφ = power factor.

V_rms = V₀/√2 for sinusoidal AC. Similarly I_rms = I₀/√2.

Transformer works on mutual induction between primary and secondary coils linked by changing magnetic flux.

Step-up transformer increases voltage: V_s/V_p = N_s/N_p > 1, so N_s > N_p. Current decreases proportionally (ignoring losses).

Large power transformers have efficiency 95-99% due to low losses (copper, iron, hysteresis, eddy current).

Energy density u_B = B²/2μ₀ in vacuum (analogous to u_E = ½ε₀E² for electric field).

Displacement current I_d = ε₀(dΦ_E/dt) completes circuit during capacitor charging and modifies Ampere's law to Ampere-Maxwell law.

Cathode rays are streams of electrons, which are negatively charged particles. Therefore, they are deflected by both electric and magnetic fields. X-rays, gamma rays, and neutrons are uncharged and are not deflected.

Capacitance (C) is a geometric property of the capacitor (C = ε₀A/d). It depends on the area of plates and the distance between them, not on the charge (Q) or voltage (V). C = Q/V, but if Q is doubled, V also doubles, keeping C constant.

By convention, electric field lines start at positive charges (high potential) and end at negative charges (low potential). They point in the direction of decreasing electric potential.

When capacitors are connected in parallel, the equivalent capacitance is the sum of individual capacitances. For three capacitors each of value C, C_eq = C + C + C = 3C.

Ohm's law states that at constant temperature, the current (I) flowing through a conductor is directly proportional to the potential difference (V) applied across its ends. V ∝ I, or V = IR.

An ammeter measures current. To measure the current flowing through a branch, the ammeter must be connected in series so that the entire current of that branch passes through it. It has very low resistance.

All three formulas are equivalent and can be derived from Joule's law of heating (H = I²Rt) by using Ohm's law V = IR. H = I²Rt = (V/R)² R t = V²t/R = VIt.

Mutual inductance (M) is a measure of the ability of one coil to induce an EMF in another. It depends on the geometry (size, shape, number of turns) of the coils, their relative positions, and the magnetic properties of the core material.

The RMS value of a sinusoidal AC is related to the peak value by V_rms = V_peak / √2. √2 ≈ 1.414. So, V_rms = 311 / 1.414 ≈ 220 V.

A transformer works on the principle of mutual induction. The voltage ratio is equal to the turns ratio: V_s/V_p = N_s/N_p. If N_s > N_p, then V_s > V_p, so it is a step-up transformer.

Impedance (Z) is the total opposition to current in an AC circuit. For a pure capacitor, the opposition is called capacitive reactance, given by Xc = 1/(ωC) = 1/(2πfC).

An ideal voltmeter should not draw any current from the circuit it is measuring. To achieve this, it must have infinite resistance so that it acts as an open circuit and measures the true potential difference.

For capacitors in series, 1/C_eq = 1/C₁ + 1/C₂. So, 1/C_eq = 1/C + 1/(2C) = (2+1)/(2C) = 3/(2C). Therefore, C_eq = 2C/3.

Power dissipated in a resistor can be calculated using P = I²R. Here, I = 2 A and R = 10 Ω. So, P = (2)² × 10 = 4 × 10 = 40 W.

The time constant (τ) of an RC circuit is the time required to charge the capacitor to approximately 63.2% of its final value (or discharge to 36.8%). It is given by the product of resistance and capacitance, τ = RC.

A DC ammeter measures average current. The average value of a symmetrical AC over a complete cycle is zero because it alternates between positive and negative values. Hence, a DC ammeter will show zero reading.

NAND and NOR gates are called universal gates because any basic logic gate (AND, OR, NOT) and any complex logic circuit can be implemented using only NAND gates (or only NOR gates).

Magnetic flux (Φ = B·A = BA cos θ) is defined as the dot product of the magnetic field vector (B) and the area vector (A). The result of a dot product is a scalar quantity.

In a pure inductor, the voltage across the inductor leads the current by 90° (or the current lags the voltage by 90°). This is because the induced EMF opposes the change in current.

A PN junction diode is a semiconductor device that allows current to flow easily in one direction (forward bias) and blocks current in the opposite direction (reverse bias). It acts as a rectifier.

Semiconductors have a negative temperature coefficient of resistance. As temperature increases, more covalent bonds break, generating more free electrons and holes. This increases the number of charge carriers, thereby increasing conductivity.

Reactance (inductive XL or capacitive XC) is the opposition to current in an AC circuit due to inductance or capacitance. It is measured in ohms (Ω), which is the same unit as resistance.

Resistance R = ρL/A. When length is doubled (L' = 2L), volume remains constant, so A' = A/2. New resistance R' = ρ(2L) / (A/2) = ρL/A × 4 = 4R.

To convert a galvanometer into a voltmeter, a high resistance is connected in series with it. This limits the current through the galvanometer and allows the combination to measure large potential differences.

For a voltmeter, V = Ig(G + R). So, 5 = (5 × 10⁻³)(50 + R). This gives 1000 = 50 + R, so R = 1000 - 50 = 950 Ω.

According to Gauss's law, the net flux through a closed surface is proportional to the charge enclosed (Φ = Q/ε₀). Changing the shape (cube instead of sphere) or moving the charge inside doesn't change the total enclosed charge. Placing a charge outside doesn't change enclosed charge. Only changing Q to 2Q changes the enclosed charge and thus the flux.

For an ideal transformer, power input = power output, so VpIp = VsIs. In a step-up transformer, Vs > Vp. Therefore, to maintain equal power, Is must be less than Ip.

For an ammeter, S = IgG / (I - Ig) = (0.001 A × 100 Ω) / (10 A - 0.001 A) ≈ 0.1 / 9.999 ≈ 0.01 Ω.

Ohm's law: V = IR, so R = V/I = 2 V / 1 A = 2 Ω.