Question

The input current to a CO-8 relay is 10 A. Determine the relay operating time for the following current tap settings (TS) and time dial settings (TDS): (a) $\mathit{T}\mathit{S}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{,}\mathbf{}\mathit{T}\mathit{D}\mathit{S}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}$(b) TS = 2.0, TDS = 1.5, (c) TS = 2.0, TDS = 7, (d) TS = 3.0, TDS = 7, and (e) TS = 12, TDS = 1.0.

Short answer

(a) The operating time of the relay corresponding to TD = 1 and $TDS=\frac{1}{2}$ is 0.07 sec.

(b) The operating time of the relay corresponding to TD = 2 and TDS = 1.5 is 0.555 sec.

(c) The operating time of the relay corresponding to TDS = 7 and relay current input multiple of current tap setting 5 is 2.97 sec.

(d) The operating time of the relay corresponding to TDS = 7 and relay current input multiple of current tap setting 3.33 is 5.1 sec.

(e) The relay will not operate and remain blocked.

Step-by-step solution

write the given data from the question:

The input current, I = 10 A

Determine the relay operating time for TS = 1.0 and TDS=12.

Consider the characteristics curve of relay from the text book’s figure 10.12.

(a)

The time dial setting is $TDS=\frac{1}{2}$.

The tap setting is TS = 1.

The tap setting is equal to the pick-up current.

Therefore, Pick up current, I_p = 1 A

Calculate the relay input current multiple of tap setting.

$$\begin{gathered} \frac{I\text{'}}{I_p}=\frac{10}{1} \\ \frac{I\text{'}}{I_p}=10 \end{gathered}$$

Since the TDS is equal to $\frac{1}{2}$choose the 0.5 curve on characteristics curve of relay.

From the curve of characteristics relay look for the operating time of relay corresponding to the relay input current multiplier.

Therefore, the operating time of the relay corresponding to TD = 1 and TDS = 1.5 is 0.07 sec.

Determine the relay operating time for TS = 2.0 and TDS = 1.5.

(b)

The time dial setting TDS = 2.

The tap setting TS = 2.

The tap setting is equal to the pick-up current.

Therefore, Pick up current I_p = 2 A.

Calculate the relay input current multiple of tap setting.

$$\begin{gathered} \frac{I\text{'}}{I_p}=\frac{10}{2} \\ \frac{I\text{'}}{I_p}=5 \end{gathered}$$

Since the TDS is equal to 1.5, therefore the operating time operating time of the relay can be calculated by taking the average of the operating time corresponding to TDS = 1 and TDS = 2.

The operating time of the relay corresponding to TDS = 1 and relay current input multiple of current tap setting 5 is 0.34 sec.

t₁ = 0.34 sec

The operating time of the relay corresponding to TDS = 2 and relay current input multiple of current tap setting 5 is 0.77 sec.

t₂ = 0.77 sec

Calculate the operating time of relay corresponding to TDS = 2 and TDS = 1.5.

$t_{1.5}=\frac{t_1+t_2}{2}$

Substitute 0.34 sec for t₁ and 0.77 sec for t₂ into above equation.

$$\begin{gathered} t_{1.5}=\frac{0.34+0.77}{2} \\ {t}_{1.5}=\frac{1.11}{2} \\ {t}_{1.5}=0.555sec \end{gathered}$$

Therefore, the operating time of the relay corresponding to TDS = 2 and TDS = 1.5 is 0.555 sec.

Determine the relay operating time for TS = 2.0, and TDS = 7.

(c)

The time dial setting, TDS = 7

The tap setting, TS = 2

The tap setting is equal to the pick-up current.

Therefore, Pick up current, I_p = 2 A

Calculate the relay input current multiple of tap setting.

$$\begin{gathered} \frac{I\text{'}}{I_p}=\frac{10}{2} \\ \frac{I\text{'}}{I_p}=5 \end{gathered}$$

The operating time of the relay corresponding to TDS = 7 and relay current input multiple of current tap setting 5 is 2.97 sec.

Determine the relay operating time for TS = 3.0, and TDS = 7.

(d)

The time dial setting, TDS = 7

The tap setting, TS = 3

The tap setting is equal to the pick-up current.

Therefore, Pick up current, I_p = 3 A

Calculate the relay input current multiple of tap setting.

$$\begin{gathered} \frac{I\text{'}}{I_p}=\frac{10}{3} \\ \frac{I\text{'}}{I_p}=3.33 \end{gathered}$$

The operating time of the relay corresponding to TDS = 7 and relay current input multiple of current tap setting 3.33 is 5.1 sec.

Determine the relay operating time for TS = 12, and TDS = 1.

(e)

The time dial setting, TDS = 1

The tap setting, TS = 12

The tap setting is equal to the pick-up current.

Therefore, Pick up current, I_p = 12 A

Calculate the relay input current multiple of tap setting.

$$\begin{gathered} \frac{I\text{'}}{I_p}=\frac{10}{12} \\ \frac{I\text{'}}{I_p}=0.833 \end{gathered}$$

Since the value of the relay input current multiple of tap setting in less than 1. Therefore, relay will not operate and remains in the blocked position.

Hence, the relay will not operate and remain blocked.