( i) When number of resistors are connected in series. The resultant resistance is given by
(ii) When number of resistors are connected in parallel the resultant resistance is given by
R1 = R2 = R3 = .... = Rn = R but = nR
Note: In the case of springs, capacitors etc. the series and parallel formulas are reversed.
e.g. : Cp = C1 + C2 + C3 +....
1 + C2 + C3 +....
SIMPLE HARMONIC MOTION
1. Two light springs have time periods of 3s and 4s with the same load. When the springs are connected in series and the same load is attached to them, the time period will be
1) 1s 2) 2.4s 3) 5s 4) 7s
2. Two springs of force constants K1 and K2 are connected to a mass 'm' as shown. The frequency of oscillation of the mass is 'f'. If both K1 and K2 are made four times their original values, the frequency of oscillation becomes
3. When a capillary tube is connected to a pressure head, V cc of water flows per second. If another tube of same length but half the radius is connected to the first in series to the same pressure head, the quantity of water flowing through them per second will be (in cc)
TRANSMISSION OF HEAT
4. Two metal rods of same length and same area of cross section are connected in series. Their conductivities are 120 and 240 SI units. The effective conductivity of the combination is
1) 150 Wm-1K-1 2) 360 Wm-1K-1 3) 200 Wm-1K-1 4) 160 Wm-1K-1
5. Three metal rods are of same length and same cross-sectional area are connected in parallel. Their conductivities are 80, 120 and 160 SI units. The effective conductivity is
1) 120 Wm-1K-1 2) 360 Wm-1K-1
3) 200 Wm-1K-1 4) 160 Wm-1K-1
6. The equivalent capacity between the points x and y in the circuit with C = 1mF is
1) 2mF 2) 3mF 3) 1mF 4) 0.5mF
7. The capacities of the three capacitors are in the ratio 1:2:3. Their equivalent capacity when connected in parallel is 60/11 mF more than they are connected in series. Their individual capacities in mF are
1) 4, 6, 7 2) 1, 2, 3 3) 2, 3, 4 4) 1, 3, 6
8. A parallel plate capacitor filled with two dielectrics of dielectric constants K1 and K2 as shown in figure. The effective capacitance is given by
9. Two cells of emfs E1 and E2 having internal resistances r1 and r2 are connected in parallel as shown. The emf and internal resistance of the equivalent source are
10. The equivalent resistance of the circuit between A and B is