Question

A resistor consists of three identical metal strips connected as shown in Fig. 26.8. If one of the strips is cut out, does the ammeter reading increase, decrease or stay the same? Why?

Short answer

The ammeter reading decreases.

Step-by-step solution

Equivalent resistance in a parallel circuit

The equation for calculating the equivalent resistance of a set of N resistors connected in parallel is:

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+...+\frac{1}{R_n}$

Determine the increase or decrease in ammeter reading by calculating the equivalent resistance

The equivalent resistance before one resistance is cut off is given as:

$$\begin{gathered} \frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+...+\frac{1}{R_n} \\ =\frac{3}{R} \\ \frac{1}{R_{eq}}=\frac{R}{3} \end{gathered}$$

After one resistor is cut off, the equivalent resistance is given as:

$$\begin{gathered} \frac{1}{R_{eq}}=\frac{1}{R}+\frac{1}{R} \\ =\frac{2}{R} \\ \frac{1}{R_{eq}}=\frac{R}{2} \end{gathered}$$

As the resistance in the circuit increases when one resistor is cut off, the current through the ammeter will decrease.

Thus, the ammeter reading will decrease.