Add.Q.(Midterm-2) - Additional Questions(Ch-26 1 Four...

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Additional Questions(Ch 23-24-25-26): 1) Four capacitors are connected as shown in the figure. (a) Find the equivalent capacitance between points a and b . (b) Calculate the charge on each capacitor if ∆ Vab = 15.0 V. Solution:
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2) In figure, the battery has a potential difference of 10 V and five capacitors each have a capacitance of 10 μ F. What is the charge on (a) capacitor 1 and (b) capacitor 2?
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Solution: (a) The potential difference across C 1 is V 1 = 10V. Thus, q 1 = C 1 V 1 =(10 µ F)(10V) = 1 . 0 × 10 - 4 C. (b) Let C = 10 µ F. We first consider the three-capacitor combination consisting of C 2 and its two closest neighbours, each of capacitance C . As seen in figure, capacitor C 2 has a serial connection with capacitor C and this combination is parallel to the other capacitor C, so we can write the equivalent capacitor as Since, the total potential difference across any number of capacitors connected in series is the sum of the potential differences across the individual capacitors and the voltages on capacitors connected in parallel are the same,
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and because of the charges on capacitors connected in series are the same, The voltage drop across this combination is Since this voltage difference is divided equally between C 2 and the one connected in series with it, the voltage difference across C 2 satisfies V 2 = V/ 2 = V 1 / 5. Thus 3) A parallel-plate capacitor of plate area A is filled with two dielectrics as in figure. Show that the capacitance is 0 1 2 2 A C d ε κ κ + = . Check this formula for limiting cases. ( Hint: Can you justify this arrangement as being two capacitors in parallel?) Solution: The capacitor can be viewed as two capacitors C 1 and C 2 in parallel, each with surface area A/ 2 and plate separation d , filled with dielectric materials with dielectric constants κ 1 and κ 2 , respectively. Thus
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4) Suppose that you wish to fabricate a uniform wire out of 1.00 g of copper. If the wire is to have a resistance of R = 0.500 Ω, and if all of the copper is to be used, what will be (a) the length and (b) the diameter of this wire?
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