A parallel– plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constant k1, k2, k3 and k4 as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by
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The potential difference (VA – VB) between the points A and B in the given figure is
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A filament bulb (500 W, 100 V) is to be used in a 230 V main suply. When a resistance R is connected in series, it works perfectly and the bulb consumes 500 W. The value of R is :
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A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a circular coil of n turns. The magnetic field at the centre of this coil of n turns will be
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A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by 60º is W. Now the torque required to keep the magnet in this new position is
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An electron is moving in a circular path under the influence of a transverse magnetic field of 3.57 × 10–2 T. If the value of e / m is 1.76 × 1011 C / kg, the frequency of revolution of the electron is
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Which of the following combinations should be selected for better tuning of an L–C–R circuit used for communication?
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A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate $\dfrac{d\overrightarrow{B}}{dt}$. Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in the figure below. Then the e.m.f. generated is
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The potential differences across the resistance, capacitance and inductance are 80 V, 40 V and 100 V respectively in an L–C–R circuit. The power factor of this circuit is
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A 100 Ω resistance and a capacitor of 100 Ω reactance are connected in series across a 220 V source. When the capacitor is 50% charged, the peak value of the displacement current is
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