Assertion (A): Potential difference across the battery can be greater than its emf.
Reason (R): When current is taken from battery \(V = \varepsilon – ir\).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true: When a battery is being charged, the terminal voltage is \(V = \varepsilon + Ir\), which is greater than its emf \(\varepsilon\). Reason (R) is also true, as it correctly describes the terminal voltage when the battery is discharging (current is taken from it). However, (R) is not the correct explanation for (A), as (A) refers to a charging scenario (where \(V > \varepsilon\)), while (R) refers to a discharging scenario (where \(V < \varepsilon\)).
Assertion (A): Current flows in conductor only when there an electric field is applied to a conductor.
Reason (R): Drift velocity of \(e^-\) decreases in presence of electric field.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: A net flow of charge (current) in a conductor requires an external electric field to give the free electrons a directional drift. Without a field, electron motion is random, leading to zero net current.
Reason (R) is false: In the presence of an electric field, free electrons experience a force and acquire a net drift velocity in the direction opposite to the electric field. Thus, drift velocity increases, it does not decrease.
Assertion (A): When a battery is supplying power to a circuit, work done by electrostatic force on electrolyte ions inside the battery is \(+ve\).
Reason (R): Electric field is directed from positive to \(-ve\) electrode inside a battery.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is false: When a battery is supplying power (discharging), positive charge moves from the negative terminal to the positive terminal inside the battery, driven by non-electrostatic (chemical) forces. The internal electrostatic field points from the positive terminal to the negative terminal. Thus, the electrostatic force on positive ions opposes their motion, doing negative work.
Reason (R) is also considered false in this context: While the *electrostatic* field due to charge separation points from positive to negative, the effective field that *drives* the current (the non-conservative EMF field) is directed from the negative to the positive electrode. If 'Electric field' in (R) implies the driving force for current, then (R) is false. Therefore, both (A) and (R) are false.
Assertion (A): In the given circuit, when switch \(S\) is ON reading of ammeter and voltmeter will increase.
Reason (R): In parallel combination net resistance will reduce.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
When switch \(S\) is ON, another resistor \(R\) is connected in parallel. The equivalent resistance of the parallel combination is \(R/2\), which is less than \(R\). Thus, the net resistance reduces (Reason R is true). The total current (ammeter reading) will increase. However, assuming an ideal voltage source, the voltage across the parallel combination (voltmeter reading) will remain constant (equal to the source EMF). Therefore, Assertion (A) is false as the voltmeter reading does not increase.
Assertion (A): In the given circuit, \(r\) is variable, value of \(I\) is maximum when \(r = R\).
Reason (R): At \(r = R\) power produced across \(R\) is minimum.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
The current in the circuit is \(I = E / (R + r)\). For \(I\) to be maximum, the denominator \((R + r)\) must be minimum. This occurs when \(r = 0\), not \(r = R\). So, Assertion (A) is false. The power produced across \(R\) is \(P_R = I^2 R = (E / (R + r))^2 R\). As \(r\) increases, \(R+r\) increases, so \(P_R\) decreases. Thus, \(P_R\) is minimum when \(r\) is maximum (approaching infinity), not at \(r = R\). So, Reason (R) is also false.
Assertion (A): If \(V_b > V_a\) current flows from \(b\) to \(a\).
Reason (R): Direction of current inside battery is always from -ve to +ve terminal.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Current in a resistor always flows from a region of higher potential to a region of lower potential. Therefore, if \(V_b > V_a\), current flows from \(b\) to \(a\). So, Assertion (A) is true. Inside a battery, the chemical processes drive positive charges from the negative terminal to the positive terminal. So, Reason (R) is true. However, the direction of current flow in a resistor (Assertion) is a fundamental concept of Ohm's law and potential difference, unrelated to the internal operation of a battery (Reason). Thus, R does not explain A.
Assertion (A): Resistance of ammeter is less than resistance of milliammeter, (If made from same galvanometer).
Reason (R): Value of shunt resistance in case of ammeter is more than a milliammeter.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
An ammeter is designed to measure larger currents than a milliammeter. To achieve a larger current range with the same galvanometer, a smaller shunt resistance is required to bypass a greater portion of the total current. A smaller shunt resistance results in a lower overall resistance for the ammeter. Thus, Assertion (A) is true. Reason (R) states the shunt resistance for an ammeter is more than a milliammeter, which is false; it must be less.
Assertion (A): When a wire is stretched, then its resistance changes directly as square of its length.
Reason (R): When wire is stretched its thickness/ radius decreases and volume remains constant.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Resistance of a wire is given by \(R = rho L/A\), where \(rho\) is resistivity, \(L\) is length, and \(A\) is cross-sectional area. When a wire is stretched, its volume \(V = AL\) remains constant. So, \(A = V/L\). Substituting this into the resistance formula, we get \(R = rho L / (V/L) = rho L^2 / V\). Since \(rho\) and \(V\) are constant, \(R propto L^2\). Thus, Assertion (A) is true. When stretched, the length increases, and for constant volume, the cross-sectional area (and thus thickness/radius) must decrease. So, Reason (R) is true. Reason (R) correctly explains why \(R propto L^2\).
Assertion (A): The brightness of light bulb in a room decreases when heavy current appliance is switched on.
Reason (R): There will be no change in brightness of bulb if source is ideal and for non ideal source voltage drop across bulb decreases.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
When a heavy current appliance is switched on, it draws a large current from the power supply. For a non-ideal source with internal resistance, this increased total current causes a larger voltage drop across the internal resistance of the source (or wiring). Consequently, the terminal voltage supplied to other devices like the light bulb decreases. A lower voltage across the bulb reduces its power output (\(P = V^2/R\)) and thus its brightness. So, Assertion (A) is true. Reason (R) correctly states that brightness remains constant for an ideal source and that voltage across the bulb decreases for a non-ideal source, which explains the dimming. Thus, Reason (R) is true and explains Assertion (A).
Assertion (A): \(100 \text{ W}\), \(60 \text{ W}\) and \(20 \text{ W}\) bulbs, each marked \(220 \text{ volt}\), are connected in series with a voltage source, then \(20 text{ W}\) bulb gives maximum illumination.
Reason (R): Resistance of filament \(20 \text{ W}\) bulb is maximum.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
The power rating of a bulb is given by \(P = V^2 / R\). For bulbs rated at the same voltage \(V\) (here \(220 text{ V}\), resistance \(R = V^2 / P\). A lower power rating implies higher resistance. Thus, the \(20 \text{ W}\) bulb has the highest resistance (Reason R is true). When bulbs are connected in series, the same current \(I\) flows through each. The power dissipated by each bulb is \(P_{actual} = I^2 R\). Since \(I\) is common, the bulb with the highest resistance will dissipate the most power and therefore glow brightest. Hence, the \(20 \text{ W}\) bulb will provide maximum illumination (Assertion A is true). Reason (R) correctly explains Assertion (A).