Capacitor C_{1} of capacitance 1 microfarad and capacitor C_{2} of capacitance 2 microfarad are separately charged fully by a common battery. The two capacitors are then separately allowed to discharge through equal resistors at time t = 0.
KEY CONCEPT : During decay of charge in R.C. circuit, I = I_{0}e^{–t/RC}
Since potential difference between the plates is same initially therefore I is same in both the cases at t = 0 and is equal to
or, t_{1} = 0.5 t_{2}
Therefore time taken for the first capacitor (1 µF) for discharging 50% of initial charge will be less.
Read the following statements carefully:
Y : The r esisti vity of a semicon ductor decreases with increase of temperature.
Z : In a conducing solid, the rate of collisions between free electrons and ions increases with increase of temperature Select the correct statement(s) from the following;
NOTE : The conductivity of a semiconductor increases with increase in temperature i.e. the resistivity decreases with increase in temperature.
In a conducting solid, the collisions become more frequent with increase of temperature.
In the circuit shown in Figure the current through
The net resistance of the circuit is 9W as shown in the following figures.
The flow of current in the circuit is as follows.
NOTE : The current divides into two equal parts if passes through two equal resistances in parallel.
Thus current through 4Ω resistor is 0.25 A.
When a potential difference is applied across, the current passing through
At 0K an insulator does not permit any current to flow through it. Option (a) is correct.
At 0K a semiconductor behaves as an insulator. Option (b) is correct.
In reverse biasing at 300 K, a very small current. flows through a pn junction diode. Option (d) is correct.
In case of metal, the current flowing will be veryvery high because a metal becomes super conductor at 0K. Option (c) is incorrect
For the circuit shown in the figure
⇒ option (a) is correct.
The potential difference accros R_{L}= potential difference accros R_{p}
_{⇒ }option (b) is incorrect.
_{⇒ }option (c) is incorrect.
The magnitude of power dissipated accross R_{2} is
Now when R_{1} and R_{2} are interchanged the equivalent resistance between R_{1} and R_{L}
∴ Potential drop across this equivalent resistance
∴ Potential difference accros
∴ The magnitude of the power dissipation in R_{L} will decrease by a factor 9 if R_{1} and R_{2 }are interchanged. (d) is the correct option.
For the resistance network shown in the figure, choose the correct option(s)
The given circuit is an extension of wheatstone bridge, therefore points P and Q are at the same potential and point S and T are also at the same potential. Therefore no current passes through PQ and ST and the circuit reduces to as shown
= 3A
As P and Q are equipotential and potential at S is less than the potential at P (potential drops across a resistance as current passes through it), therefore V_{S} < V_{Q}.
Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5 kg water by 40 K. This heater is replaced by a new heater having two wires of the same material, each of length L and diameter 2d. The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by 40 K?
When resistances are connected in series
From (i) and (ii) t_{2} = 2 min. Therefore (b) is correct.
When resistance are connected in parallel
From (i) and (iii) t_{2} = 0.5 min
∴ (d) is correct
Two ideal batteries of emf V_{1} and V_{2} and three resistances R_{1}, R_{2} and R_{3} are connected as shown in the figure. The current in resistance R_{2} would be zero if
Applying KVL in MNOPQAM
V_{1}  iR_{1} + V_{2}  iR_{3}=0
Applying KVL in NOPQN
If V_{1} = V_{2} then R_{1} = R_{3} = R_{2}∴ (a) is correct option.
If V_{1} = V_{2} then R_{1} = R_{3} = 2R_{2}∴ (b) is correct option. (R_{2} can have any value as there is no current flowing through d) If V_{1} = 2V_{2} then 2R_{3} = R_{1} ∴ (c) is incorrect option.
If 2V_{1} = V_{2} then R_{3} = 2R_{1} = R, ∴ (d) is correct option.
In an aluminium (Al) bar of square cross section, a square hole is drilled and is filled with iron (Fe) as shown in the figure. The electrical resistivities of Al and Fe are 2.7 × 10^{–8} Ω m and 1.0 × 10^{–7} Ω m, respectively. The electrical resistance between the two faces P and Q of the composite bar is
An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black–body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non–uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is(are) true?
With the use of filament and the evaporation involved, the filament will become thinner thereby decreasing the area of crosssection and increasing the resistance. Therefore the filament will consume less power towards the end of life.
As the evaporation is nonuniform, the area of crosssection will be different at different crosssection. Therefore temperature distribution will be nonuniform. The filament will break at the point where the temperature is maximum.
When the filament temperature is higher it emits light of lower wavelength or higher band of frequencies.
In the circuit shown below, the key is pressed at time t = 0. Which of the following statement(s) is(are) true?
At t=0, Capacitors act as short circuit and voltmeter display –5v At t = µ, Capacitor acts as open circuit and no current flows through voltmeter ( ∴ very high resistance of voltmeter) so it display +5V. (a) is the correct option
(b) is the correct option
∴ (c) is the correct option After a long time no current flows since both capcitor and voltmeter do not allow current to flow.
∴ (d) is the correct option.
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