# Problem: In the figure R1 = 2.75R, the ammeter resistance is zero, and the battery is ideal. What multiple of ε/R gives the current in the ammeter?

###### FREE Expert Solution

Let the current through resistor R be i.

From the figure, the voltage across the ammeter is zero making the current in the bottom resistors to be the same.

The current through the battery is then 2i.

The voltage drop across the bottom resistors, VR = iR.

Equivalent resistance for 2 resistors in parallel:

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

Equivalent resistance for resistors in series:

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

From these equations, the equivalent resistance of the circuit is:

$\begin{array}{rcl}{\mathbf{R}}_{\mathbf{e}\mathbf{q}}& \mathbf{=}& \mathbf{\left[}\frac{\mathbf{\left(}\mathbf{2}\mathbf{.}\mathbf{75}\mathbf{R}\mathbf{\right)}\mathbf{\left(}\mathbf{R}\mathbf{\right)}}{\mathbf{2}\mathbf{.}\mathbf{75}\mathbf{R}\mathbf{+}\mathbf{R}}\mathbf{\right]}\mathbf{+}\mathbf{\left[}\frac{\mathbf{\left(}\mathbf{R}\mathbf{\right)}\mathbf{\left(}\mathbf{R}\mathbf{\right)}}{\mathbf{R}\mathbf{+}\mathbf{R}}\mathbf{\right]}\\ & \mathbf{=}& \frac{\mathbf{2}\mathbf{.}\mathbf{75}{\mathbf{R}}^{\mathbf{2}}}{\mathbf{3}\mathbf{.}\mathbf{75}\mathbf{R}}\mathbf{+}\frac{{\mathbf{R}}^{\mathbf{2}}}{\mathbf{2}\mathbf{R}}\\ & \mathbf{=}& \frac{\mathbf{2}\mathbf{.}\mathbf{75}\mathbf{R}}{\mathbf{3}\mathbf{.}\mathbf{75}}\mathbf{+}\frac{\mathbf{R}}{\mathbf{2}}\end{array}$

###### Problem Details

In the figure R1 = 2.75R, the ammeter resistance is zero, and the battery is ideal. What multiple of ε/R gives the current in the ammeter?

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 Resistors and Ohm's Law concept. You can view video lessons to learn Resistors and Ohm's Law. Or if you need more Resistors and Ohm's Law practice, you can also practice Resistors and Ohm's Law practice problems.