Maharashtra State BoardHSC Science (Electronics) 11th
Advertisement Remove all ads

Answer the following question. Show that if Z = AB, △ZZ=△AA+△BB - Physics

Answer in Brief

Answer the following question.

Show that if Z = `"A"/"B"`, `(triangle"Z")/"Z" = (triangle"A")/"A" + (triangle "B")/"B"`

Advertisement Remove all ads


Errors in divisions:

Suppose, Z = `"A"/"B"` and measured values of A and B are (A ± ΔA) and (B ± ΔB) then,

Z ± ΔZ = `("A" +- triangle"A")/("B"+-triangle"B")`

∴ Z`(1 +- (triangle"Z")/"Z") = ("A"[1 +-(Δ"A"//"A")])/("B"[1 +-(Δ"B"//"B")])`

`= "A"/"B" xx [1 +-(Δ"A"//"A")]/[1 +-(Δ"B"//"B")]`

As, `(triangle"B")/"B" ≪ 1,` expanding using Binomial theorem,

`"Z"(1 +- (triangle"Z")/"Z") = "Z" (1 +- (triangle"A")/"A") xx (1  bar+ (Δ"B")/"B")`   ....`(because "A"/"B" = "Z")`

∴ `1 +- (Δ"Z")/"Z" = 1 +- (Δ"A")/"A" bar+ (Δ"B")/"B" +- (Δ"A")/"A" xx (Δ"B")/"B"`

Ignoring term `(Δ"A")/"A" xx (Δ"B")/"B", (Δ"Z")/"Z" = +-  (Δ"A")/"A"  bar+  (Δ"B")/"B"`

This gives four possible values of `(Δ"Z")/"Z"` as

`(+ (Δ"A")/"A" - (Δ"B")/"B"), (+(Δ"A")/"A" + (Δ"B")/"B"), (-(Δ"A")/"A" - (Δ"B")/"B") and (-(Δ"A")/"A" + (Δ"B")/"B")`

∴ Maximum relative error of `(Δ"Z")/"Z" +- ((Δ"A")/"A" + (Δ"B")/"B")`

Thus, when two quantities are divided, the maximum relative error in the result is the sum of relative errors in each quantity.

  Is there an error in this question or solution?
Advertisement Remove all ads


Balbharati Physics 11th Standard Maharashtra State Board
Chapter 1 Units and Measurements
Exercises | Q 2. (v) | Page 14
Advertisement Remove all ads
Advertisement Remove all ads

View all notifications

      Forgot password?
View in app×