Assertion (A): Two identical cells are connected in (a) series (b) parallel then maximum power transferred to the load is same in both cases.
Reason (R): Value of load resistance for maximum power transfer for series and parallel combination of cells are same.
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. For two identical cells (emf \(E\), internal resistance \(r\)), in series, \(E_{\text{eq}} = 2E\) and \(r_{\text{eq}} = 2r\). Max power \(P_{\text{max,s}} = (2E)^2 / (4 \cdot 2r) = E^2 / (2r)\). In parallel, \(E_{\text{eq}} = E\) and \(r_{\text{eq}} = r/2\). Max power \(P_{\text{max,p}} = E^2 / (4 \cdot r/2) = E^2 / (2r)\). The maximum power is indeed the same. Reason (R) is false. For series, the load resistance for max power is \(R_L = 2r\), while for parallel, it is \(R_L = r/2\). These are not the same.
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
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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): 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): 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): A car engine can be started more easily on a warm day than on a cold day.
Reason (R): EMF of battery is more on a cold day.
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
It is a common observation that starting a car engine is more difficult on a cold day due to several factors including increased viscosity of engine oil and reduced battery performance. So, Assertion (A) is true. On a cold day, the chemical reactions inside a battery slow down, leading to an increase in its internal resistance and a decrease in its effective capacity, rather than an increase in EMF. The EMF generally tends to slightly decrease or remain similar. So, Reason (R) is false.
Assertion (A): In real battery total chemical energy lost in the battery can not be obtained at load resistance.
Reason (R): Two heaters with different resistance are connected in parallel. Higher resistance heater will glow more.
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
Assertion (A) is true due to the internal resistance of real batteries, which dissipates some chemical energy as heat. Reason (R) is false; for parallel connections, power \( P = V^2 / R \), so the heater with *lower* resistance will glow more.
Assertion (A): Terminal potential difference of a cell is always less than its emf.
Reason (R): Potential drop across internal resistance of cell increases terminal potential difference.
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. The terminal potential difference \( V \) is equal to emf \( E \) when no current is drawn (open circuit) and can be greater than \( E \) during charging. Reason (R) is false. The potential drop across internal resistance (\( Ir \)) actually decreases the terminal potential difference (\( V = E - Ir \) for discharging).
Assertion (A): A larger dry cell has higher emf.
Reason (R): The emf of a dry cell is proportional to its size.
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
The electromotive force (EMF) of a cell depends only on the nature of the electrodes and electrolyte, not its size. Size affects internal resistance and current capacity. Both assertion and reason are incorrect.
Assertion (A): A car battery is of \(12\text{ V}\). Eight dry cells of \(1.5\text{ V}\) connected in series can give \(12\text{ V}\). Still such cells are not used in starting a car.
Reason (R): It is easier to start a car engine on a warm day than on a rainy day.
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: \(8 times 1.5\text{ V} = 12\text{ V}\). Dry cells have high internal resistance and cannot provide the high current needed to start a car. Reason (R) is also true, as engine oil is less viscous on a warm day. However, (R) does not explain (A).
Assertion (A): When identical cells are connected in parallel to the external load, the effective emf increases.
Reason (R): All the cells will be sending unequal current to the external load in the same direction.
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
When identical cells are connected in parallel, the effective EMF remains the same as that of a single cell, while the current capacity increases. Thus, Assertion (A) is false. For identical cells, current distribution should be equal. Thus, Reason (R) is also false.