Questions: For a current transformer iL/iS = TP/TS. a. Solve for iL. b. Solve for IS c. Find iL when iS=1.5 amperes, TP=1600, and TS=100. iL = (TS iS)/TP iL = TS/(TP iS) iL = TP/(TS iS) iL = (TP iS)/TS

For a current transformer iL/iS = TP/TS.
a. Solve for iL.
b. Solve for IS
c. Find iL when iS=1.5 amperes, TP=1600, and TS=100.
iL = (TS iS)/TP
iL = TS/(TP iS)
iL = TP/(TS iS)
iL = (TP iS)/TS

Transcript text: For a current transformer $\frac{i_{L}}{i_{S}}=\frac{T_{P}}{T_{S}}$. a. Solve for $i_{L}$. b. Solve for $\mathrm{I}_{\mathrm{S}}$ c. Find $\mathrm{i}_{\mathrm{L}}$ when $\mathrm{i}_{\mathrm{S}}=1.5$ amperes, $\mathrm{T}_{\mathrm{P}}=1600$, and $\mathrm{T}_{\mathrm{S}}=100$. $i_{L}=\frac{T_{S} i_{S}}{T_{P}}$ $i_{L}=\frac{T_{S}}{T_{P} i_{S}}$ $i_{L}=\frac{T_{P}}{T_{S} i_{S}}$ $i_{L}=\frac{T_{P} i_{S}}{T_{S}}$

Solution

Solution Steps

Step 1: Solve for \( i_L \)

Given the equation for a current transformer:

\[ \frac{i_{L}}{i_{S}} = \frac{T_{P}}{T_{S}} \]

To solve for \( i_L \), multiply both sides by \( i_S \):

\[ i_L = \frac{T_P}{T_S} \cdot i_S \]

Step 2: Solve for \( i_S \)

Starting from the same equation:

\[ \frac{i_{L}}{i_{S}} = \frac{T_{P}}{T_{S}} \]

To solve for \( i_S \), multiply both sides by \( i_S \) and then divide by \( \frac{T_P}{T_S} \):

\[ i_S = \frac{T_S}{T_P} \cdot i_L \]

Step 3: Find \( i_L \) when \( i_S = 1.5 \) amperes, \( T_P = 1600 \), and \( T_S = 100 \)

Using the formula derived in Step 1:

\[ i_L = \frac{T_P}{T_S} \cdot i_S = \frac{1600}{100} \cdot 1.5 \]

Calculate \( i_L \):

\[ i_L = 16 \cdot 1.5 = 24 \text{ amperes} \]

Final Answer

a. \( i_L = \frac{T_P}{T_S} \cdot i_S \)

b. \( i_S = \frac{T_S}{T_P} \cdot i_L \)

c. \( i_L = 24 \text{ amperes} \)

\[ \boxed{a. \, i_L = \frac{T_P}{T_S} \cdot i_S} \] \[ \boxed{b. \, i_S = \frac{T_S}{T_P} \cdot i_L} \] \[ \boxed{c. \, i_L = 24 \text{ amperes}} \]

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