Figure shows two identical triode tubes connected in paralle. The anodes are connected together, the grids are connected together and the cathodes are connected together. Show that the equivalent plate resistance is half of the individual plate resistance, the equivalent mutual conductance is double the individual mutual conductance and the equivalent amplification factor is the same as the individual amplification factor.
(##HCV_VOL2_C41_E01_049_Q01##)

Two cells of same emf but different internal resistance are connected in parallel so as to send current in same direction. STATEMENT-1 : The equivalent emf of the combination is equal to individual emf of each cell. and STATEMENT-2 : The equivalent emf is the arithmetic mean of the individual emfs.

Two parallel plate vacuum capacitors have areas A_1 and A_2 and equal plate spacing d . Show that when the capacitors are connected in parallel, the equivalent capacitance is the same as for a single capacitor with plate area A_1+A_2 and spacing d .

Figure 6.32 shows a meter bridge in the (which is nothing but a particle wheastone bridge), consisting of two resistors X and Y together in parellel with a meter long constantan wire of uniform cross section. with the help of a movable contact d , one can change the ratio of resistance of the two segments of the wire until a sensitive galvanometer G connected across b and D shows no deflection. The null point is found to be at a distance of 33.7 cm . The resistor Y is shunted by a resistance of 12 Omega , and the null point is found to shift by a distance of 18.2 cm . Determine the resistance of X and Y .

A rectangular conducting loop consists of two wires on two opposite sides of length l joined together by rods of length d. The wires are each of the same material but with cross-sections differing by a factor of 2. The thicker wire has a resistance R and the rods are of low resistance, which in turn are connected to a constant voltage source V_0 . The loop is placed in a uniform magnetic field B at 45^@ to its plane. Find tau , the torque exerted by the magnetic field on the loop about an axis through the centres of rods.

The circuit shows a resistance, R=0.01Omega and inductance L=3mH connected to a conducting rod PQ of length l=1m which can slide on a perfectly conducting circular arc of radius l with its center at P. Assume that friction and gravity are absent and a constant uniform magnetic field b=0.1T exists as shown in the figure. At t=0, the circuit is seitched on a simultaneously an external torque is applied on the rod so that it rotates about P with a constant angular velocity omega =2 rad//sec . Find the magnitude of this torque (inN-m) at t=(0.3In 2) second.

Four rods of material X and three rods of material Y are connected as shown in figure. All the rods are of identical lengths and cross-sectional area. Given thermal resistance of rod of material X, R_(x) = R and thermal conductivities of materials are related by relation K_(Y) = 2K_(X) . {:(,"Column-I",,"Column-II"),((A),"Thermal resistance between B and E" ,(p),(500)/(13).^(@)C ),((B),"Thermal resistance between A and F" ,(q),(700)/(13).^(@)C ),((C),"Temperature of junction B" ,(r),(2R)/(3)), ((D),"Temperature of junction D" ,(s),(13R)/(6)):}

Two metallic rods of same area of cross section, having lengths in ratio 2:3 and ratio of thermal conductivities 2:3 are connected in series across a temperature difference as shown in figure. The temperature of the junction (theta_0) is