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:

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

Ohm's law:

$\overline{){\mathit{V}}{\mathbf{=}}{\mathit{i}}{\mathit{R}}}$

**A)**

When switch S is open R_{2} and R_{3} are connected in series.

R_{eq} = R_{2} + R_{3} = 6.00 + 3.00 = 9.00Ω

i = ε/R_{eq} = 71.0/9.00 = 7.89 A

In the circuit shown below, ε = 71.0 V, R_{1} = 4.00 Ω, R_{2} = 6.00 Ω, R_{3} = 3.00 Ω.

A) What is the potential difference *V*_{a}* _{b}* between points

B) What is the potential difference *V*_{a}* _{b}* between points

C) For the 4.00 Ω resistor, calculate the current through the resistor with *S* open.

D) For the 4.00 Ω resistor, calculate the current through the resistor with *S* closed.

E) For the 4.00 Ω resistor, calculate the current through the resistor with *S* closed.

F) For the 6.00 Ω resistor, calculate the current through the resistor with *S* closed.

G) For the 3.00 Ω resistor, calculate the current through the resistor with *S* open.

H) For the 3.00 Ω resistor, calculate the current through the resistor with *S* closed.

I) For each resistor, does the current increase or decrease when *S* is closed?

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