If two resistors${\mathit{R}}_{\mathbf{1}}$ and$\left(R_2>R_1\right)$ are connected in parallel as shown in Fig. Q, which of the following must be true? In each case justify your answer.

(a) ${\mathit{I}}_{\mathbf{1}}\mathbf{=}{\mathit{I}}_{\mathbf{2}}$.

(b) ${\mathit{I}}_{\mathbf{3}}\mathbf{=}{\mathit{I}}_{\mathbf{4}}$.

(c) The current is greater in${\mathit{R}}_{\mathbf{1}}$ than in ${\mathit{R}}_{\mathbf{2}}$.

(d) The rate of electrical energy consumption is the same for both resistors.

(e) The rate of electrical energy consumption is greaterrole="math" localid="1663843965569" ${\mathit{R}}_{\mathbf{2}}$ in than in ${\mathit{R}}_{\mathbf{1}}$.

(f)${\mathit{V}}_{\mathbf{c}\mathbf{d}}\mathbf{=}{\mathit{V}}_{\mathbf{e}\mathbf{f}}\mathbf{=}{\mathit{V}}_{\mathbf{a}\mathbf{b}}$

(g) Point c is at higher potential than point d.

(h) Pointf is at higher potential than at point e.

(i) Pointc is at higher potential than at point e.

In a parallel circuit, all components are connected in such a way that the potential drop across all the components is the same.

$R_1$and$R_2$ are in parallel where the current is not the same in both resistors. And as $R_2>R_1$, hence$I_1>I_2$ where $I\alpha \frac{1}{R}$.

The combination of $R_1$and $R_2$are in series with the remaining circuit where the current in series is the same. The current enters equal to the current out. (conservation of charges theorem)

As discussed in part (a).

The consumed power P is inversely proportional to the resistance when the voltage is the same $P=\frac{V^2}{R}$. And as $R_2>R_1$, hence $P_1>P_2$.

As discussed in part (d), $P_1>P_2$.

In parallel, the voltage across is the same for each individual resistance$R_1$ and $R_2$.

The current flows from higher potential energy to lower potential energy, therefore, the potential at c is higher than d.

As discussed in part (g), the current flows from higher potential energy to lower potential energy, therefore,$e$ has a higher potential than f.

Thus, the statements are False, True, True, False, False, True, True, False, and False respectively.