Question

72 • series circuits
figure 5 - 88

1. by observing the meters in figure 5 - 88, determine the types of failures in the circuits and which components have failed.

Explanation:

Step1: Analyze circuit (a)

In a series - circuit, if ammeter reads 0 A and voltmeters show non - zero values across some components, it may indicate an open - circuit. Here, ammeter reads 0 A, and voltmeters show voltage across \(R_1\) and \(R_2\). This implies that there is an open - circuit in the path of the current flow. Since there is voltage across \(R_1\) and \(R_2\), the open - circuit is likely in \(R_3\) or \(R_4\) or the connection between them.

Step2: Analyze circuit (b)

The ammeter reads 333 mA. In a series circuit with a supply voltage of 10 V and all resistors of 100 \(\Omega\), the total resistance \(R_{total}=5\times100\ \Omega = 500\ \Omega\). According to Ohm's law \(I=\frac{V}{R}\), the expected current \(I=\frac{10\ V}{500\ \Omega}=20\ mA\). The high current value indicates a short - circuit. Since the voltmeter across \(R_4\) reads 0 V, \(R_4\) is likely short - circuited.

Answer:

In circuit (a), there is an open - circuit, likely in \(R_3\) or \(R_4\) or the connection between them. In circuit (b), \(R_4\) is short - circuited.