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# Problem: In the circuit shown below, ε = 71.0 V, R1 = 4.00 Ω, R2 = 6.00 Ω, R3 = 3.00 Ω.A) What is the potential difference Vab between points a and b when the switch S is open?B) What is the potential difference Vab between points a and b when the switch S is closed?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?

###### FREE Expert Solution

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:

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

A)

When switch  S is open R2 and R3 are connected in series.

Req = R2 + R3 = 6.00 + 3.00 = 9.00Ω

i = ε/Req = 71.0/9.00 = 7.89 A

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###### Problem Details

In the circuit shown below, ε = 71.0 V, R1 = 4.00 Ω, R2 = 6.00 Ω, R3 = 3.00 Ω.

A) What is the potential difference Vab between points a and b when the switch S is open?

B) What is the potential difference Vab between points a and b when the switch S is closed?

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?

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Solving Resistor Circuits concept. You can view video lessons to learn Solving Resistor Circuits. Or if you need more Solving Resistor Circuits practice, you can also practice Solving Resistor Circuits practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Jerousek's class at UCF.