In the given circuit, switch S is open initially. If C=2 μ F and V=3 V, then find the heat produced (in μ J ) in the circuit after closing the switch.

Question

In the given circuit, switch S is open initially. If C=2 μ F and V=3 V, then find the heat produced (in μ J ) in the circuit after closing the switch. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/27767bc43e87e726c7d911ef1e3bd9d8-.png" /> Ui=(1/2) C ⋅((V/2))2 ⋅ 2 ; Uf=(1/2) C V2=(C V2/2) W text Cell =V ⋅ Δ q=V ⋅(C V-(C V/2))=(C V2/2) Now, Ui+W text cell =Uf+H ∴ H=(C V2/4)=(2 × 9/4)=4.50

Q. In the given circuit, switch $S$ is open initially. If $C = 2 μ F$ and $V = 3 V$ , then find the heat produced (in $μ J$ ) in the circuit after closing the switch.

$U_{i} = \frac{1}{2} C \cdot (\frac{V}{2})^{2} \cdot 2; U_{f} = \frac{1}{2} C V^{2} = \frac{C V ^{2}}{2}$
$W_{Cell} = V \cdot Δ q = V \cdot (C V - \frac{C V}{2}) = \frac{C V ^{2}}{2}$
Now, $U_{i} + W_{cell} = U_{f} + H$
$∴ H = \frac{C V ^{2}}{4} = \frac{2 \times 9}{4} = 4.50$

Q. In the given circuit, switch S is open initially. If C=2μF and V=3V, then find the heat produced (in μJ ) in the circuit after closing the switch.

Ui​=21​C⋅(2V​)2⋅2;Uf​=21​CV2=2CV2​ WCell ​=V⋅Δq=V⋅(CV−2CV​)=2CV2​ Now, Ui​+Wcell ​=Uf​+H ∴H=4CV2​=42×9​=4.50

Q. In the given circuit, switch $S$ is open initially. If $C = 2 μ F$ and $V = 3 V$ , then find the heat produced (in $μ J$ ) in the circuit after closing the switch.

$U_{i} = \frac{1}{2} C \cdot (\frac{V}{2})^{2} \cdot 2; U_{f} = \frac{1}{2} C V^{2} = \frac{C V ^{2}}{2}$
$W_{Cell} = V \cdot Δ q = V \cdot (C V - \frac{C V}{2}) = \frac{C V ^{2}}{2}$
Now, $U_{i} + W_{cell} = U_{f} + H$
$∴ H = \frac{C V ^{2}}{4} = \frac{2 \times 9}{4} = 4.50$