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(a) Three resistors of resistances $1 \Omega, 2 \Omega$ and $3 \Omega$ are combined in series. What is the total resistance of the combination?
(b) If the combination is connected to a battery of emf $12 \mathrm{~V}$ and negligible internal resistance, obtain the potential drop across each resistor.
(b) If the combination is connected to a battery of emf $12 \mathrm{~V}$ and negligible internal resistance, obtain the potential drop across each resistor.
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Verified Answer
(a) Given, $\mathrm{R}_1=1 \Omega, \mathrm{R}_2=2 \Omega, \mathrm{R}_3=3 \Omega, \mathrm{R}_{\mathrm{s}}=$ ?
(b) $\varepsilon=12 \mathrm{~V}, \mathrm{~V}_1=$ ?, $\mathrm{V}_3=$ ?
(a) By formula, $\mathrm{R}_{\mathrm{s}}=\mathrm{R}_1+\mathrm{R}_2+\mathrm{R}_3$ $=1+2+3=6 \Omega$
(b) By relation, $\mathrm{I}=\mathrm{E} / \mathrm{R}=12 / 6=2 \mathrm{~A}$
\& $\mathrm{V}=\mathrm{RI}$
$$
\begin{aligned}
&\mathrm{V}_1=\mathrm{R}_1 \mathrm{I}=1 \times 2=2 \mathrm{~V} \\
&\mathrm{~V}_2=\mathrm{R}_2 \mathrm{I}=2 \times 2=4 \mathrm{~V} \\
&\mathrm{~V}_3=\mathrm{R}_3 \mathrm{I}=3 \times 2=6 \mathrm{~V}
\end{aligned}
$$
(b) $\varepsilon=12 \mathrm{~V}, \mathrm{~V}_1=$ ?, $\mathrm{V}_3=$ ?
(a) By formula, $\mathrm{R}_{\mathrm{s}}=\mathrm{R}_1+\mathrm{R}_2+\mathrm{R}_3$ $=1+2+3=6 \Omega$
(b) By relation, $\mathrm{I}=\mathrm{E} / \mathrm{R}=12 / 6=2 \mathrm{~A}$
\& $\mathrm{V}=\mathrm{RI}$
$$
\begin{aligned}
&\mathrm{V}_1=\mathrm{R}_1 \mathrm{I}=1 \times 2=2 \mathrm{~V} \\
&\mathrm{~V}_2=\mathrm{R}_2 \mathrm{I}=2 \times 2=4 \mathrm{~V} \\
&\mathrm{~V}_3=\mathrm{R}_3 \mathrm{I}=3 \times 2=6 \mathrm{~V}
\end{aligned}
$$
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