Question

To measure currents in Figure \({\rm{21}}{\rm{.49}}\), you would replace a wire between two points with an ammeter. Specify the points between which you would place an ammeter to measure the following: (a) the total current; (b) the current flowing through \({{\rm{R}}_{\rm{1}}}\); (c) through \({{\rm{R}}_{\rm{2}}}\) ; (d) through \({{\rm{R}}_{\rm{3}}}\) . Note that there may be more than one answer to each part.

Short answer

1. The total current obtained is: \(2.14{\rm{ }}\Omega \)
2. The ammeter is connected to measure the current flowing through the value\({R_1}\).
3. The current flowing through the point\({R_2}\)is obtained as:\(214{\rm{ }}\Omega \).
4. The ammeter is connected to measure the current flowing through the value \({R_3}\).

Step-by-step solution

Define Circuit

An electronic circuit is made up of individual electronic components including resistors, transistors, capacitors, inductors, and diodes that are linked by conductive wires or traces.

Evaluating total current

a.

The points by which we connect the ammeter is used to measure the total current.

Terminal voltage can be evaluated as:

\(R{\rm{ }} = {\rm{ }}\frac{{{R_1}({R_2} + {R_3})}}{{{R_1} + ({R_2} + {R_3})}}\)

The value here is:

\(\begin{align}{}{R_2} + {R_3}{\rm{ }} &= {\rm{ }}6 + 1.5\\{\rm{ }} &= {\rm{ }}7.5{\rm{ }}\Omega \end{align}\)

The total current then obtained is:

\(\begin{align}{}R{\rm{ }} &= {\rm{ }}\frac{{(7.5)(3)}}{{(7.5) + (3)}}\\ &= {\rm{ }}2.14{\rm{ }}\Omega \end{align}\)

The diagram drawn is:

Evaluating the current flowing through the point

b.

The current is flowing through the value \({R_1}\).

So, the ammeter has been connected to measure the current flowing through the value of \({R_1}\), has been drawn.

Evaluating the current flowing through the point

(c)

The current is flowing through the value \({R_2}\).

So, the ammeter has been connected to measure the current flowing through the value of \({R_2}\), has been drawn.

The calculation is then obtained as: \(214{\rm{ }}\Omega \).

Evaluating the current flowing through the point

d.

The current is flowing through the value \({R_3}\).

So, the ammeter has been connected to measure the current flowing through the value of\({R_3}\), has been drawn.

Therefore, we get:

1. The total current is: \(2.14{\rm{ }}\Omega \)
2. The ammeter is connected to measure the current flowing through the value\({R_1}\).
3. The current flowing through the point\({R_2}\)is:\(214{\rm{ }}\Omega \).
4. The ammeter is connected to measure the current flowing through the value \({R_3}\).