Question

A battery-powered set of five patio lanterns is connected in series. An ammeter measures the current through the battery as 0.75 A. The total resistance of the circuit is 52 0. (a) Calculate the voltage drop across the battery. (b) Calculate the voltage drop across each load.

Answer 1

Answer:

(a) 39 V

(b) 7.8 V

Explanation:

(a) Neglecting the internal resistance of the battery, the voltage drop (V) across the battery is found from Ohm's law as follows;

V = IR                -------------------------(i)

Where;

I = current through the battery

R = total resistance of the circuit.

From the question;

I = 0.75A

R = 52.0Ω

Substitute the values of I and R into equation (i)

=> V = 0.75 x 52.0

=> V = 39Volts

Therefore, the voltage drop across the battery is 39 Volts

(b) Since the set of lanterns is connected in series, then the same current flows through each of the lanterns. Also, since the lanterns are identical, the resistance ($R_{L}$) of each of them is given by the total resistance (R = 52.0Ω) divided by the number of lanterns. i.e

$R_{L}$ = $\frac{52.0}{5}$

$R_{L}$ = 10.4Ω          [Each lantern has a resistance of 10.4Ω]

The current flowing through them is the same as the current (I = 0.75A) flowing the circuit.

Therefore, using Ohm's law, the voltage drop ($V_L$)across each load (lantern) is

$V_L$ = I x $R_{L}$

$V_L$ = 0.75 x 10.4

$V_L$ = 7.8Volts

Therefore, the voltage drop across each load is 7.8 Volts