This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Question 12: Energy consumed by a bread toaster Step 1: Identify the given values. Current, I = 4.0 A Voltage, V = 240.0 V Time, t = 1 minute Step 2: Convert time to seconds. t = 1 minute × 60 seconds1 minute = 60 s Step 3: Use the formula for electrical energy consumed. Energy (E) is given by the product of voltage (V), current (I), and time (t): E = V × I × t Step 4: Substitute the values and calculate the energy. E = 240.0 V × 4.0 A × 60 s E = 960 W × 60 s E = 57600 J Express in scientific notation: E = 5.76 × 10^4 J Comparing with the given options: (a) 5.78 × 10^4 J (b) 3.60 × 10^3 J (c) 3.87 × 10^4 J (d) 6.48 × 10^5 J The calculated value 5.76 × 10^4 J is closest to option (a). There might be a slight rounding difference in the option. The energy consumed by the toaster is a) 5.78 × 10^4 J. --- Question 13: Equivalent capacitance of three capacitors in series Step 1: Identify the given information. Number of capacitors, n = 3 Capacitance of each capacitor, C_1 = C_2 = C_3 = C Connection type: Series Step 2: Recall the formula for equivalent capacitance in series. For capacitors connected in series, the reciprocal of the equivalent capacitance (C_eq) is the sum of the reciprocals of individual capacitances: (1)/(C_eq) = (1)/(C_1) + (1)/(C_2) + (1)/(C_3) Step 3: Substitute the given capacitances and solve for C_eq. (1)/(C_eq) = (1)/(C) + (1)/(C) + (1)/(C) (1)/(C_eq) = (1+1+1)/(C) (1)/(C_eq) = (3)/(C) To find C_eq, take the reciprocal of both sides: C_eq = (C)/(3) The equivalent capacitance is a) C/3. --- Question 14: Hooke's Law proportionality Step 1: Recall Hooke's Law. Hooke's Law states that the force (F) required to extend or compress a spring by some distance (x) is directly proportional to that distance, provided the elastic limit is not exceeded. Mathematically, this is expressed as: F = kx Where k is the spring constant. Step 2: Apply Hooke's Law to the given problem. The problem states that the force needed to elongate an elastic object by an amount "S" is proportional to "S". According to Hooke's Law, the force (F) is directly proportional to the elongation (S). F S The force needed to elongate an elastic object by an amount "S" is proportional to a) S.