Question

In following diagram boxes may contain resistor or battery or any other element.

Then determine in each case

(a) $E . m . f .$ of battery.

(b) Battery is acting as a source or load.

(c) Potential difference across each battery.

(d) Power input to the battery or output by the battery.

(e) The rate at which heat is generated inside the battery.

(f) The rate at which the chemical energy of the cell is consumed or increased.

(g) Potential difference across the box

(h) Electric power output across the box.

Accepted Answer

From the given circuit diagram $(A)$ ;

(a) Emf of the battery $= 10 V$

(b) Since, current is flowing towards the box and away from the given battery, therefore, the battery is acting as a source.

(c) Potential difference across battery $V = E - I r (r =$ internal resistance of the battery $)$

$\Rightarrow V = 10 - 1 \times 1 = 9 V .$

(d) Power is given by the battery, so, power, $P = V I = 9 \times 1 = 9 W$ .

(e) The rate at which heat is generated inside the battery due to its resistance is given by, $I^{2} r = 1 \times 1 \times 1 = 1 W$ .

(f) The rate at which chemical energy is consumed is $P = E I = 10 \times 1 = 10 W .$

(g) Potential difference across box, $V = E - I r = 10 - 1 \times 1 = 9 V .$

(h) Since power is used by the element in the box so electric power output the box is $- 9 W$ .

From the given circuit diagram $(B)$ ,

(a) Emf of the battery $= 10 V .$

(b) Since, current is flowing away from the box and towards the given battery, so the given battery is acting as load.

(c) Potential difference across battery is, $V = E + I r = 10 + 1 \times 1 = 11 V$ .

(d) Power input to the battery is, $P = V I = 11 \times 1 = 11 W .$

(e) The rate at which heat is generated in the battery is given by, $I^{2} r = 1 \times 1 \times 1 = 1 W$ .

(f) The rate at which chemical energy is increased of the cell is, $P = E I = 10 \times 1 = 10 W .$

(g) Potential difference across the box, $V = E + I r = 10 + 1 \times 1 = 11 V .$

(h) Since the box contains a source element so the power output the box is, $+ 11 W .$

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