Question
Derive an expression for decrease in potential energy when a charge flows through an external resistance in a circuit.
✓
Answer
i. Consider a resistor AB connected to a cell in a circuit with current flowing from A to B.
ii. The cell maintains a potential difference V between the two terminals of the resistor, higher potential at $A$ and lower at $B$.
iii. Let Q be the charge flowing in time $\Delta t$ through the resistor from A to B .
iv. The potential difference $V$ between the two points $A$ and $B$, is equal to the amount of work (W) done to carry a unit positive charge from $A$ to $B$.
$\therefore V =\frac{W}{Q}$
v. The cell provides this energy through the charge $Q$, to the resistor $A B$ where the work is performed.
vi. When the charge $Q$ flows from the higher potential point $A$ to the lower potential point $B$, there is decrease in its potential energy by an amount
$\Delta U = QV = I \Delta tV$
where $I$ is current due to the charge $Q$ flowing in time $\Delta t$.
ii. The cell maintains a potential difference V between the two terminals of the resistor, higher potential at $A$ and lower at $B$.
iii. Let Q be the charge flowing in time $\Delta t$ through the resistor from A to B .
iv. The potential difference $V$ between the two points $A$ and $B$, is equal to the amount of work (W) done to carry a unit positive charge from $A$ to $B$.
$\therefore V =\frac{W}{Q}$
v. The cell provides this energy through the charge $Q$, to the resistor $A B$ where the work is performed.
vi. When the charge $Q$ flows from the higher potential point $A$ to the lower potential point $B$, there is decrease in its potential energy by an amount
$\Delta U = QV = I \Delta tV$
where $I$ is current due to the charge $Q$ flowing in time $\Delta t$.
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