number 3 A battery with an emf of 9.00 V is connected to a 75-ohm resistor and a

Question

number 3

A battery with an emf of 9.00 V is connected to a 75-ohm resistor and an ammeter. If the ammeter reads 119 mA, what is the internal resistance of the battery? 2. In 2nd Grade, you learned about money. More specifically, you got those problems where Jimmy bought a pack of gum for 59 cents, gave the cashier a dollar, and you had to not only say how much change Jimmy got but how to make that change using the fewest number of coins. Now you are in college. You have a drawer full of 30-ft and 75-ohm resistors and need to combine them in such a way as to make a 55-ft resistor. Use the rules for equivalent resistance in series and parallel to come up with a combination of 30-ft and 75-ohm resistors that has an equivalent resistance of 55-ohm. Your challenge is to do this using the fewest possible number of resistors. 3. When connected in series, a pair of resistors (/?i and R2) draw a total power of 80.0 mW and carry a current of 0.100 A. When connected in parallel, t hey draw 640 mW of power with a current of 0.800 A (his is the current measured before it has split up into the parallel branches). Find the values of the two resistances (i.e., R_1 = ? and R_2 = ?). 4. ohmve resistors are connected as shown in the diagram. Two of the resistors are identical (R), but their resistance is not known. If the equivalent resistance for the full network is 75 ohm, find the value of the resistance R.

Explanation / Answer

series combination of resistances is given as , Rs = R1 + R2

Given that : Power in series = Ps = 80 mW = 0.08 Watt

is = current = 0.1 A

using the formula

Ps = is2 Rs

0.08 = (0.1)2 (R1 + R2 )

R1 + R2 = 8                                  

R1 = 8 - R2                                      eq-1

Parallel combination of resistances is given as , Rp = R1 R2 / (R1 + R2) = R1 R2 / 8

Given that : Power in series = Pp = 640 mW = 0.64 Watt

ip = current = 0.8 A

using the formula

Pp = ip2 Rp

0.64 = (0.8)2 (R1 R2 / 8)

R1 R2 = 8

using eq-1

(8 - R2 ) R2 = 8

R2 = 1.17   or 6.83

R1 = 6.83 or 1.17

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