Chapter 32: Q. 48 (page 926)

The small transformers that power many consumer products produce a $12.0 V_{r m s}$ , $60 H z$ emf. Design a circuit using resistors and capacitors that uses the transformer voltage as an input and produces a $6.0 V_{r m s}$ output that leads the input voltage by $45 °$ .

Short Answer

Expert verified

The $R_{1} = 6 Ω, R_{2} = 2.5 Ω a n d C = 3.12 \times 10^{- 4} F$ .

Step by step solution

Step 1:Given Information

We are given that small transformer produces voltage $12 V_{r m s}, 60 H z$ emf.

We have to design the circuit which have $6 V_{r m s}$ output that leads the input voltage by $45 °$ .

Step 2:Formula Used

As the capacitor voltage is lead by the resistor voltage . So, the input must ne in between the resistors and the phase difference is of $45 °$ .

Now, $Z_{R} = Z_{C}$

then $V_{C} = V_{R} = \frac{12}{\sqrt{2}}$

which gives $V_{C} = V_{R} = 8.5 V$ .

Step 3:Simlify

Let $R_{1}$ be the resistor needed to make the voltage $6 V_{r m s}$

then $\frac{R_{1}}{6} = \frac{Z_{R}}{8.5}$

On simplifying we get,

$R_{1} = 0.71 Z_{R}$

let role="math" localid="1650018615730" $Z_{R} = 8.5 Ω$ then

On solving, $R_{1} = 6 Ω a n d R_{2} = 2.5 Ω$

and $Z_{C} = 8.5 Ω = \frac{1}{ω C}$

where $ω = 2 π \times 60$

On solving we get,

$C = 3.12 \times 10^{- 3} F$

Hence, the resistor $R_{1} = 6 Ω a n d R_{2} = 2.5 Ω$ and the capacitor $C = 3.12 \times 10^{- 3} F$ .

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The small transformers that power many consumer products produce a $12.0 V_{r m s}$ , $60 H z$ emf. Design a circuit using resistors and capacitors that uses the transformer voltage as an input and produces a $6.0 V_{r m s}$ output that leads the input voltage by $45 °$ .

Short Answer

Step by step solution

Step 1:Given Information

Step 2:Formula Used

Step 3:Simlify

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The small transformers that power many consumer products produce a12.0Vrms, 60Hzemf. Design a circuit using resistors and capacitors that uses the transformer voltage as an input and produces a 6.0Vrms output that leads the input voltage by 45°.

Short Answer

Step by step solution

Step 1:Given Information

Step 2:Formula Used

Step 3:Simlify

One App. One Place for Learning.

Most popular questions from this chapter

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The small transformers that power many consumer products produce a $12.0 V_{r m s}$ , $60 H z$ emf. Design a circuit using resistors and capacitors that uses the transformer voltage as an input and produces a $6.0 V_{r m s}$ output that leads the input voltage by $45 °$ .