Physics — Force, Machines, Light, Sound, Electricity & Modern Physics — Practice

Question 1

Two resistors of 4 Ω and 12 Ω are connected (a) in series, (b) in parallel, across a 24 V battery. Find the total resistance and total current in each case.

Accepted Answer

(a) SERIES: R_total = 4 + 12 = 16 Ω. Current I = V/R = 24/16 = 1.5 A. (b) PARALLEL: 1/R_total = 1/4 + 1/12 = 3/12 + 1/12 = 4/12. R_total = 12/4 = 3 Ω. Current I = V/R = 24/3 = 8 A. Note: Parallel gives much lower resistance and higher current. Check (b) using shortcut: R = (4 × 12)/(4 + 12) = 48/16 = 3 Ω ✓.

Question 2

A concave lens of focal length 20 cm is used. An object is placed 30 cm from the lens. Find: (a) the image distance, (b) magnification, (c) nature of the image.

Accepted Answer

Concave lens: f = −20 cm (negative for diverging lens). Object: u = −30 cm. LENS FORMULA: 1/v − 1/u = 1/f. 1/v = 1/f + 1/u = 1/(−20) + 1/(−30) = −3/60 − 2/60 = −5/60. v = −12 cm. (a) Image distance = 12 cm on the SAME side as the object (virtual image). (b) m = v/u = (−12)/(−30) = +0.4. (c) Since m is positive and less than 1: image is VIRTUAL, ERECT, and DIMINISHED. It forms 12 cm to the left of the lens (same side as object). This is always the case for a concave lens with a real object.

Question 3

100 g of ice at 0°C is added to 200 g of water at 60°C in an insulated container. Find the final temperature of the mixture. (Specific heat of water = 4.2 J/g°C, Latent heat of fusion of ice = 336 J/g)

Accepted Answer

Step 1: Heat available from water cooling from 60°C to 0°C: Q_available = 200 × 4.2 × 60 = 50,400 J. Step 2: Heat needed to melt all ice: Q_melt = 100 × 336 = 33,600 J. Since Q_available (50,400) > Q_melt (33,600), all ice melts. Step 3: Remaining heat after melting = 50,400 − 33,600 = 16,800 J. This heat raises the temperature of the now-melted water (100 g ice → 100 g water at 0°C). Total water = 100 + 200 = 300 g. 16,800 = 300 × 4.2 × T_f. T_f = 16,800 / 1,260 = 13.33°C. FINAL TEMPERATURE = 13.3°C.

Practice — Physics — Force, Machines, Light, Sound, Electricity & Modern Physics

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