Current

 

Electric Current and Voltage Division Rule

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Electric Current Division Rule

This rule finds application when we have to find the current passing through each impedance when these are connected in parallel. Let us say, two impedances Z₁ and Z₂ are connected in parallel as shown below.
A current I passes and divides in I₁ and I₂ at the junction of these two impedances as shown. I₁ and I₂ pass through Z₁ and Z₂ respectively. Our aim is to determine I₁ and I₂ in terms of I, Z₁ and Z₂. As Z₁ and Z₂ are connected in parallel, voltage drop across each will be same. Hence, we can write Also applying Kirchoff’s current law at junction, we get We have two equations and can determine I₁ and I₂.

From (1), we have Putting this in (2), we get Or, Or, Or, We have Putting value of I₁, we get

Thus, we have determined I₁ and I₂ in terms of I, Z₁ and Z₂. This rule is applied as follows. Suppose we have to determine I₁. We proceed as Applying above rule, we will get Let us apply this rule to some problems. Let Z₁ = 1 + j3, Z₂= 3 + j5 and I = 10 amps. Applying current divison rule, we will have Where I₁ = current passing through Z₁. Putting given numerical values, we get Similarly, The other way to find I₂ is as I₂ = I – I₁ = 10-6.5 + j0.5 = 3.5 + j0.5. This is how we can apply current division rule.

Voltage Division Rule

Voltage division rule finds application when we have to find voltage across some impedance. Let us suppose that the impedance Z₁, Z₂, Z₃,…..Z_n are connected in series and voltage source V is connected across them as shown below. Our aim is to find voltage across some impedance, say, Z₃. We see that Z₁, Z₂, Z₃ ….Z_n are connected in series. Hencem effective impedance Zeff as seen by the voltage is given by Current passing the circuit is given by This current is passing through all the impedances connected in series. Hence, voltage across Z₃ is given by Similarly, voltage across Z₁ will be given by In general, we can write Where k = 1, 2, 3 ,….n. This is called voltage divion rule and frequently used to determine voltage across some impedance. We can write this rule in words as given below. Voltage across some impedance Impedances Z₁, Z₂, Z₃ ,…….Z_n should be connected in series. We will solve one problem of finding voltages across impedances using voltage divisio rule.

Problem

impedance Z₁=2+j4, Z₂ = 3+j7 AND Z₃ = 6+j2 are connected in series. Across these impedance connected in series, a voltage source of 100V is connected as shown below. Determine the voltage across each impedance. SOLUTION: Applying voltage division rule, we get Similarly, We can also determine V_z3 as follows. Actually, we can determine voltage across any impedance in this way if voltages across all other remaining impedances are known. When we Z₁=Z₂=Z₃=…….Z_n, voltage across each impedance is given by V₁=V₂=V₃=………..V_n. Thus voltage will be same across each impedance and it equals V/n, that is, source voltage divided number of impedances connected in series.