Question

resistor a = 50 ω
resistor b = 75 ω
resistor c = 150 ω
total current in parallel circuit = 0.60 a
current flowing through b = ____ a
current flowing through a = ____ a
total voltage = ____ v
voltage drop on b = ____ v
total resistance = ____ ω
voltage drop on c = ____ v
voltage drop on a = ____ v
current flowing through c = ____ a

Explanation:

Step1: Calculate total resistance

For resistors in parallel, \(\frac{1}{R_{total}}=\frac{1}{R_A}+\frac{1}{R_B}+\frac{1}{R_C}\).
Substitute \(R_A = 50\Omega\), \(R_B=75\Omega\), \(R_C = 150\Omega\):
\(\frac{1}{R_{total}}=\frac{1}{50}+\frac{1}{75}+\frac{1}{150}=\frac{3 + 2+1}{150}=\frac{6}{150}=\frac{1}{25}\), so \(R_{total}=25\Omega\).

Step2: Calculate total voltage

Using \(V = I\times R\), with \(I = 0.60A\) and \(R_{total}=25\Omega\), \(V=0.60\times25 = 15V\).

Step3: Calculate current through each resistor

Since in parallel \(V = V_A=V_B=V_C = 15V\).
For resistor \(A\): \(I_A=\frac{V}{R_A}=\frac{15}{50}=0.3A\).
For resistor \(B\): \(I_B=\frac{V}{R_B}=\frac{15}{75}=0.2A\).
For resistor \(C\): \(I_C=\frac{V}{R_C}=\frac{15}{150}=0.1A\).

Answer:

Current flowing through \(B = 0.2A\)
Current flowing through \(A = 0.3A\)
Total voltage \(= 15V\)
Voltage drop on \(B = 15V\)
Total resistance \(= 25\Omega\)
Voltage drop on \(C = 15V\)
Voltage drop on \(A = 15V\)
Current flowing through \(C = 0.1A\)