What is the relationship between the time period (T) and frequency (f) of a wave? MCQ with Answer and Explanation

Explanation:
Resonance in series LCR circuit occurs when X_L = X_C, i.e., ωL = 1/(ωC) ⇒ ω = 1/√(LC). At this frequency, impedance is minimum (Z=R), current maximum, and circuit is purely resistive. Memory tip: 'Resonance: X_L = X_C; ω₀ = 1/√(LC); series: Z_min, parallel: Z_max'. This AC circuit concept is frequently tested in competitive exams. Always distinguish series and parallel resonance conditions; competitive exams often test series LCR resonance fundamentals.

Explanation:
Resistance of a bulb is R = V^2 / P. The 60W bulb has a higher resistance than the 100W bulb. When connected in series, the exact same current (I) flows through both. The power consumed (which determines brightness) is given by P = I^2R. Since the 60W bulb has higher resistance (R), it consumes more power and glows brighter.

Explanation:
v_esc ∝ √(1/R). If R→R/4, v_esc ∝ √(4) = 2. So 2v_e.