The storage battery of a car has an emf of 12 V. If the internal resistance of the battery is 0.4?, what is the maximum current that can be drawn from the battery?

A battery of emf 10 V and internal resistance 3 ? is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?

(I) Threeresistors1?,2?,and3?arecombinedinseries.Whatisthetotal resistance of thecombination? (II) Ifthecombinationisconnectedtoabatteryofemf12Vandnegligibleinternal resistance, obtain the potential drop across eachresistor.

(I) Threeresistors2?,4?and5?arecombinedinparallel.Whatisthetotal resistance of thecombination? (II) If the combination is connected to a battery of emf 20 V and negligible internal resistance,determinethecurrentthrougheachresistor,andthetotalcurrentdrawn from the battery.

At room temperature (27.0 °C) the resistance of a heating element is 100 ?. What is the temperature of the element if the resistance is found to be 117 ?, given that the temperature coefficient of the material of the resistor is

A negligibly small current is passed through a wire of length 15 m and uniform cross- section 6.0 × 10^-7 m², and its resistance is measured to be 5.0 ?. What is the resistivity of the material at the temperature of the experiment?

A silver wire has a resistance of 2.1 ? at 27.5 °C, and a resistance of 2.7 ? at 100 °C. Determine the temperature coefficient of resistivity of silver.

Aheating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds toa steady value of 2.8 A. What is the steady temperature of the heating element if the room temperature is 27.0 °C? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1.70 × 10^-4 °C ^-1.

Determine the current in each branch of the network shown in fig 3.30:

(I) Inametrebridge[Fig.3.27],thebalancepointisfoundtobeat39.5cmfromthe end A, when the resistor Y is of 12.5 ?. Determine the resistance of X. Why are the connections between resistors in a Wheatstone or meter bridge made of thick copper strips? (II) Determine the balance point of the bridge above if X and Y areinterchanged. (III) Whathappensifthegalvanometerandcellareinterchangedatthebalancepointof the bridge? Would the galvanometer show anycurrent?

A storage battery of emf 8.0 V and internal resistance 0.5 ? is being charged by a 120 V dc supply using a series resistor of 15.5 ?. What is the terminal voltage of the battery during charging? What is the purpose of having a series resistor in the charging circuit?

In a potentiometer arrangement, a cell of emf 1.25 V gives a balance point at 35.0 cm length of the wire. If the cell is replaced by another cell and the balance point shifts to63.0 cm, what is the emf of the second cell?

The number density of free electrons in a copper conductor estimated in Example 3.1 is 8.5 × 10²⁸ m^-3. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 × 10^-6 m² and it is carrying a current of 3.0 A.

The earth’s surface has a negative surface charge density of 10^-9 C m^-2. The potential difference of 400 kV between the top of the atmosphere and the surface results (due to the low conductivity of the lower atmosphere) in a current of only 1800 A over the entire globe. If there were no mechanism of sustaining atmospheric electric field, how much time (roughly) would be required to neutralise the earth’s surface? (This never happens in practice because there is a mechanism to replenish electric charges, namely the continual thunderstorms and lightning in different parts of the globe). (Radius of earth = 6.37 × 10⁶ m.)

(I) Sixlead-acidtypeofsecondarycellseachofemf2.0Vandinternalresistance0.015 ? are joined in series to provide a supply to a resistance of 8.5 ?. What are the current drawn from the supply and its terminalvoltage? (II) Asecondarycellafterlongusehasanemfof1.9Vandalargeinternalresistanceof 380 ?. What maximum current can be drawn from the cell? Could the cell drive the starting motor of acar?

Two wires of equal length, one of aluminium and the other of copper have the same resistance. Which of the two wires is lighter? Hence explain why aluminium wires are preferred for overhead power cables. (?_Al = 2.63 × 10^-8 ? m, ?_Cu = 1.72 × 10^-8 ? m, Relative density of Al = 2.7, of Cu = 8.9.)

Whatconclusioncanyoudrawfromthefollowingobservationsonaresistormadeof alloymanganin? Current A Voltage V Current A Voltage V 0.2 3.94 3.0 59.2 0.4 7.87 4.0 78.8 0.6 11.8 5.0 98.6 0.8 15.7 6.0 118.5 1.0 19.7 7.0 138.2 2.0 39.4 8.0 158.0

Choose the correct alternative: (I) Alloysofmetalsusuallyhave(greater/less)resistivitythanthatoftheirconstituent metals. (II) Alloysusuallyhavemuch(lower/higher)temperaturecoefficientsofresistancethan puremetals. (III) Theresistivityofthealloymanganinisnearlyindependentof/increasesrapidlywith increase oftemperature. (IV) Theresistivityofatypicalinsulator(e.g.,amber)isgreaterthanthatofametalbya factor of the order of(10²²/10³).

(I) GivennresistorseachofresistanceR,howwillyoucombinethemtogetthe(i) maximum (ii) minimum effective resistance? What is the ratio of the maximum to minimumresistance? (II) Giventheresistancesof1?,2?,3?,howwillbecombinethemtogetan equivalent resistance of (i) (11/3) ? (ii) (11/5) ?, (iii) 6 ?, (iv) (6/11)?? (III) Determine the equivalent resistance of networks shown in Fig.3.31.

Determine the current drawn from a 12 V supply with internal resistance 0.5 ? by the infinite network shown in Fig. 3.32. Each resistor has 1 ? resistance.

Figure 3.33 shows a potentiometer with a cell of 2.0 V and internal resistance 0.40 ? maintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of 1.02 V (for very moderate currents up to a few mA) gives a balance point at 67.3 cm length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of 600 k? is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf e and the balance point found similarly, turns out to be at 82.3 cm length of the wire. (I) What is the value e? (II) What purpose does the high resistance of 600 k?have? (III) Is the balance point affected by this highresistance? (IV) Is the balance point affected by the internal resistance of the drivercell? (V) Wouldthemethodworkintheabovesituationifthedrivercellofthepotentiometer had an emf of 1.0 V instead of 2.0V? (f ) Would the circuit work well for determining an extremely small emf, say of the order of a few mV (such as the typical emf of a thermo-couple)? If not, how will you modify the circuit?

Figure 3.34 shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor R = 10.0 ? is found to be 58.3 cm, while that with the unknown resistance X is 68.5 cm. Determine the value of X. What might you do if you failed to find a balance point with the given cell of emf e?

Figure 3.35 shows a 2.0 V potentiometer used for the determination of internal resistance of a 1.5 V cell. The balance point of the cell in open circuit is 76.3 cm. When a resistor of 9.5 ? is used in the external circuit of the cell, the balance point shifts to 64.8 cm length of the potentiometer wire. Determine the internal resistance of the cell.