We wish to measure the voltage V_b produced by high voltage power supply, but ou

Question

We wish to measure the voltage V_b produced by high voltage power supply, but our voltmeter has the limited range of +2 to -2 volts. To make the measurement we use the voltage divider circuit shown below, containing a big resistor R_1 and a small resistor R_2. If, for example, R_2 is 1000 times smaller than R1t then the voltage across R_2 is 1000 times smaller than that across R_1. By measuring the small voltage across the small resistor we can use this result to determine the big voltage v_b. What current i flows through the circuit? Express your answer in terms of V_b. Find the formula for V_b in terms of V_2, the voltage measured across the small resistor. Find a formula for V_b in terms of V_2, R_1 and R_2, assuming R_1 > > R_2, so that you can replace (R_1 + R_2) by R_1 in the equation for i. Our voltmeter reads V_2 =.24 volts. What was V_b?

Explanation / Answer

a.) Current I = total voltage / total resistance = Vb / (R1 + R2 ) =  Vb / (106 +103 )

Therefore I = Vb / 1001000 = 9.99000999 x 10-7 Vb

b.) Vb = V1 + V2

But V1 / V2 = R1 / R2 = 1000 => V1 = 1000V2

So, Vb = 1000V2 + V2 = 1001 V2

c.) Vb = V1 + V2

But V1 / V2 = R1 / R2    = > V1 = V2 (R1 / R2 )

So,  Vb = V1 + V2 = V2 (R1 / R2 ) + V2 = V2 ( R1 + R2 ) / R2

Since R1 > > R2 , R1 + R2 ~ R1  ;

So, Vb ~ V2 (R1 / R2 )

I = Vb / (R1 + R2 ) ~ Vb / R1

d.) Vb ~ V2 (R1 / R2 ) = 0.24 x 106 / 103 = 240 Volts

Vb ~ 240 Volts

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