Equivalent resistance for resistors in parallel:

$\overline{)\frac{\mathbf{1}}{{\mathbf{R}}_{\mathbf{eq}}}{\mathbf{=}}\frac{\mathbf{1}}{{\mathbf{R}}_{\mathbf{1}}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{R}}_{\mathbf{2}}}{\mathbf{+}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{R}}_{\mathbf{n}}}}$

or for 2 resistors:

$\overline{){{\mathbf{R}}}_{{\mathbf{eq}}}{\mathbf{=}}\frac{{\mathbf{R}}_{\mathbf{1}}{\mathbf{R}}_{\mathbf{2}}}{{\mathbf{R}}_{\mathbf{1}}\mathbf{+}{\mathbf{R}}_{\mathbf{2}}}}$

Equivalent resistance for resistors in series:

$\overline{){{\mathbf{R}}}_{{\mathbf{eq}}}{\mathbf{=}}{{\mathbf{R}}}_{{\mathbf{1}}}{\mathbf{+}}{{\mathbf{R}}}_{{\mathbf{2}}}{\mathbf{+}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{+}}{{\mathbf{R}}}_{{\mathbf{n}}}}$

**A.**

R_{1} and R_{2} are in parallel.

R_{12} is in series with R_{3} and R_{4}

R_{A} = R_{1}R_{2}/(R_{1} + R_{2}) + R_{3} + R_{4}

Consider the network of four resistors shown in the diagram, where *R*_{1} = 2.00Ω , *R*_{2} = 5.00Ω , *R*_{3} = 1.00Ω , and *R*_{4} = 7.00Ω . The resistors are connected to a constant voltage of magnitude *V*. (Figure 1)

A. Find the equivalent resistance *R** _{A}* of the resistor network.

B. Two resistors of resistance *R*_{5} = 3.00Ω and *R*_{6} = 3.00Ω are added to the network, and an additional resistor of resistance *R*_{7} = 3.00Ω is connected by a switch, as shown in the diagram..(Figure 2) Find the equivalent resistance *R*_{B} of the new resistor network when the switch is open.

C. Find the equivalent resistance *R*_{C} of the resistor network described in Part B when the switch is closed.

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