Shrinivas Academy Physics Tutorial Sheet No: 3.06 (Current Electricity & Ohm’s Law)

By Sanjeet Singh Adarsh ( 9822793601 sadarsh@iitbombay.org ) ---------------------------------------- Level 1 ------------------------------------------

Q1. I. E. Irodov Prob. No 3.150. Q2. I. E. Irodov Prob. No 3.151. Q3. A certain wire has a time varying current as i = io + αt where io = 10 A

and α = 4 A/s. Find the charged passed through the wire in 10 s. Q4. A Galvanometer of coil resistance 20 Ω and full scale deflection current of

1 mA is to be used as an ammeter for measuring currents upto 10 A. Find the shunt resistance required for this purpose and also find the equivalent resistance of the device. If the same Galvanometer is to be used as a voltmeter for measuring upto 10 V then what is the resistance required to be put in series with the coil?

Q5. I. E. Irodov Prob. No 3.152. Q6. I. E. Irodov Prob. No 3.173. Q7. I. E. Irodov Prob. No 3.174. Q8. I. E. Irodov Prob. No 3.175. Q9. Find the resistance of a solid frustum of a cone of cross-section radii a

and b (b > a). The length of the specimen is l and the resistivity of the material is given to be ρ.

Q10. I. E. Irodov Prob. No 3.176. Q11. I. E. Irodov Prob. No 3.177. Q12. I. E. Irodov Prob. No 3.178. Q13. I. E. Irodov Prob. No 3.179. Q14. A thick spherical shell has radii a and b (b > a) and is made of a material

of resistivity ρ. If the PD between the inner and the outer spherical surfaces are maintained as Vo find the current density in the shell as a function of the distance r from the centre.

---------------------------------------- Level 2 ------------------------------------------

Q1. The two plane faces of a solid annular cylindrical pipe are maintained at a potential difference of Vo. The inner and the outer radii of the pipe are a and b (b > a). The resistivity of the material varies radially as ρ = α/r where α is some suitable physical constant. What is the total electric current passing through this pipe? 21V

1Ω 8Ω

16Ω

4Ω

6Ω

5Ω 5V

2V

Q2. For the circuit shown in the figure find the currents in all the resistors. The required values are all shown in the figure itself.

Q3. I. E. Irodov Prob. No 3.180. Q4. I. E. Irodov Prob. No 3.181. Q5. I. E. Irodov Prob. No 3.182. Q6. I. E. Irodov Prob. No 3.183.

Q7. I. E. Irodov Prob. No 3.184. Q8. I. E. Irodov Prob. No 3.185. Q9. Find the equivalent resistance between the points a and b for the circuits

shown in the 3 figures below. Each resistor has a resistance of R.

Q10. I. E. Irodov Prob. No 3.186. Q11. I. E. Irodov Prob. No 3.187. Q12. In a charging process of a capacitor after how many time constants the

energy stored in the capacitor reaches half of the maximum value? Q13. A capacitor of capacity C initially charged to a PD of Vo is discharged

through a resistor R. What is the heat generated in the resistor in one time constant?

Q14. Find the current flowing out of the battery for the circuit shown in the figure besides?

Q15. A capacitor of capacity C with initial charge as qo is connected to a battery of emf Vo through a resistor R. What is the charge on the capacitor as a function of time?

Q16. Find the charge accumulated on the capacitor as a function of time for the circuit shown in the figure. All required values are given in the figure itself.

Q17. Find the charge accumulated on the capacitor as a function of time for the circuit shown in the figure. All required values are given in the figure itself.

Q18. I. E. Irodov Prob. No 3.189. Q19. I. E. Irodov Prob. No 3.190. Q20. I. E. Irodov Prob. No 3.191. Q21. I. E. Irodov Prob. No 3.193. Q22. Consider the RC circuit shown in the figure. Now, S2 is

closed with S1 opened till the capacitor gets fully charged. Then S2 is opened and S1 closed till the charge reduces to half of the maximum. This takes a time t1. Now S1 is opened again and S2 closed till the charge on the capacitor is three-fourth of the maximum. This takes a time t2. Find t1/t2.

Q23. I. E. Irodov Prob. No 3.203. Q24. I. E. Irodov Prob. No 3.205. Q25. Nine wires each of resistance R are joined to form

a prism as shown in the figure. Find the effective resistance between (a) a and d (b) a and b?

a b a b

Vo

R R C

Vo

R 6R C 3R

b a

R4 Vo R1 R3 R2

S1 R

ηR S2

a e d

b f c