Lecture 17 Problems & Solution(1) [1] What is the magnitude of the current flowing in the circuit shown in Fig. 2? [2] A copper wire has resistance 5 Ohms. Given that the resistivity of silver is 85 percent of the resistivity of copper, what is the resistance of a silver wire three times as long with twice the diameter? [3] A resistor draws a current of 1A when connected across an ideal 3V battery. Another resistor draws a current of 2A when connected across an ideal 3V battery. What current do the two resistors draw when they are connected in series across an ideal 3V battery? [4] What is the effective resistance of the resistor network shown in Fig. 4? [5] In the circuit shown in Fig. 5 what is the current labelled I? [6] In the circuit shown in Fig. 5 what is the magnitude of the voltage difference between points A and B? [7] In Fig. 2 what is the magnitude of the current flowing through the 1 Ohm resistor? [Q] Find the equivalent resistance between points a and b in Figure 8.27. (b) A potential difference of 34V is applied between points a and b in Figure 28.28. Calculate the current in each resistor. [8] In the capacitor network of Fig. 8 the charge on the 2 micro Farad capacitor is 2 micro Coulombs. What is the charge on the 1 micro Farad capacitor? [9] In the capacitor network of Fig. 8 the voltage across the 4 micro Farad capacitor is 1 Volt. What is the voltage across the 2 micro Farad capacitor? [10] An air capacitor consisting of two closely spaced parallel plates has a capacitance of 1000 pF. The magnitude of the charge on each plate is 4 micro Coulombs. If a dielectric material with dielectric constant K = 2 is inserted between the plates of the capacitor, what will happen to the energy stored in the capacitor? (The charge remains unchanged.) [11] What is the effective capacitance of the capacitor network in Figure 9? [Q] When two capacitors are connected in parallel, the resulting combination has a total capacitance . When the same two capacitors are connected in series, the resulting combination has a total capacitance . What are the capacitances of the two capacitors? [12] A certain wire has resistance R. What is the resistance of a second wire, made of the same material, which is half as long and has 1/3 the diameter? [13] A heating element is made by maintaining a potential difference of 60.0 V along the length of a Nichrome wire with radius 0.945 mm and a resistivity of 5.00 × 10−7 Ω m. If the element dissipates 5000 W, what is its length in m? [Q] A certain amount of copper is formed into a cylindrical rod of length L and has a resistance measured between the two ends of R. If the rod is compressed to half of its original length while maintaining its original volume, what is the new resistance of the rod? [14] Find the total energy stored in the three capacitors assuming that the battery has an emf of 12 V and that the capacitors all have a capacitance of 4 μF. Answer:432 μJ [Q] Four capacitors, each with a capacitance of 10 F, are connected as shown in the gure to a 10 V battery. What is the potential dierence across capacitor C1? [Q] In the circuit shown below, what is the potential dierence across the 3 resistor?