# Voltage And Current Dividers Electrical Assignment Help

## The Voltage Divider

A sub circuit known as the voltage divider occurs so often that it is worthy of special attention.The part of the circuit which is properly the voltage divider consists of resistors R1 and R2 and is enclosed by the dotted line. The input terminals of the voltage divider are connected, in this case, to an ideal voltage source, and the output terminals are connected to an ideal voltmeter. For a given voltage at the input terminals, what voltage is measured by the ideal voltmeter at the output? Let us answer this question using the node method of solution. Designating the output voltage as VOUT, we use Kirchhoff’s current law for the node at the upper output terminal:

Vin-Vout/R1 – Vout/R2 = 0

Solving, we have

Vout = Vin R2/R1+R2 (voltage divider)

This is the general voltage-divider formula; we recommend that it be memorized. Very often formal circuit analysis can be avoided when a circuit can be recognized as a simple voltage divider.

The voltage appearing across R1 is equal to VIN minus the voltage across R2. Thus the voltage across R, is VIN[1 – R2/(R1 + R2)] = VIN[R1/(R1 + R2)]. The symmetry between this expression and Eq. (2.28) is readily apparent: the expression for the voltage across R2 has R2 in its numerator; that for the voltage across R1 has R1 in its numerator.

The Voltage Divider Circuit.

The voltage divider circuit. The voltage indicated by the ideal voltmeter is a simple fraction of the input voltage.

In using the voltage-divider formula, one must be careful to include all resistances which are present in the circuit. For instance, in Fig. 2.34 we have a circuit very similar to that of Fig. 2.33, but the voltmeter is not ideal. On the contrary, it is more like an actual physical voltmeter, which consists of a large internal resistance in parallel with an ideal voltmeter. The circuit of Fig. 2.34 is nonetheless a voltage divider, but R3 must be regarded as being in parallel with R2 so that the voltage-divider formula may be used. The output voltage for Fig. 2.34 is therefore

Vout = Vin (R2||R3)/(R2||R3) + R1

Physical Voltmeter

A voltage divider circuit with a load. The resistance R3 of the non ideal voltmeter must be taken into account in calculating the output voltage.

Expanding R211R3′ we have

Vout = Vin R2R3/R2R3 + R1R2 + R1R3

### Example

Find the voltage indicated by the ideal voltmeter in the circuit.

Ideal Voltmeter in the Circuit

### Solution

We observe that the voltage across the terminals of R, is VI> regardless of the value of R, (provided only that R, of. 0). Using the voltage-divider formula, we have

V = V1 R3/R2 + R3

### Example

A de lighting system contains ten bulbs connected in series; 120-V power is supplied to the system, which is designed to use ten 50-W 12-V bulbs. However, a mistake is made and someone replaces one of the 50-W bulbs with a 100-W 12 V bulb. How much power is actually supplied to the 100-W bulb?

### Solution

The 50-W bulbs each have resistance

R50  = (12)2/50 = 2.88  and the 100-W bulb has resistance R100 =(12)2/100=1.44

The circuit thus contains a total resistance of RT = 9(2.88) + 1.44 = 27.36 0, and the voltage across the 100-W bulb is, from the voltage-divider formula,

V100 =  R100/RT. 120 = 1.44/27.36. 120 = 6.32 V

Thus the power delivered to the 100-W bulb is

P100 = (V100)2/R100 = (6.32)2/1.44 = 27.7 W

### The Current Divider

A similar subcircuit that can sometimes be recognized in larger circuits is the current divider. In this figure the parallel combination of R1 and R2 gives a net resistance of R1R2/(R1 + R2) across the current source. Therefore by Ohm’s law VA – VB = IIN R1R2/(R1 + R2). The values of I1 and I2 can now be found from I1 = (VA – VB)/R1 and I2 = (VA – VB)/R2

I1 = IIN R2/R1 + R2  and  I2 = IIN R1/R1+R2

A Current Divider Circuit.

A current divider circuit. The values of I, and ‘2 are given by Eqs. (2.31) and (2.32).

Note that although there is a similarity between these equations and Eq. (2.28) for the voltage divider, there is also a subtle difference. In Eq. (2.28) the fraction appearing in the expression for the voltage across R2 has R2 in its numerator. In Eq. (2.32) the fraction in the expression for the current through R2 has R1, not R2, in the numerator. This is as one would expect intuitively; as R, is increased, more current is diverted to the path through R2·

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Posted on April 25, 2016 in Introduction To Circuit Analysis
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