To analyze the behavior of the circuit you've described, we need to consider the properties of inductance and resistance in both the coil and the resistor. When the switch is opened, the circuit undergoes a change that affects the current and voltage across each component. Let's break down the situation step by step.
Understanding the Circuit Before the Switch is Opened
Initially, when the switch is closed, the coil and the resistor are connected to a 200 V DC supply. The total current flowing through the circuit can be calculated using Ohm's Law and the concept of parallel circuits.
Calculating the Total Current
In a parallel circuit, the voltage across each component is the same. Therefore, the voltage across both the coil and the 200 Ω resistor is 200 V. The current through the 200 Ω resistor can be calculated as:
- Current through the 200 Ω resistor, IR = V / R = 200 V / 200 Ω = 1 A
Next, we need to find the current through the coil. The coil has a resistance of 80 Ω and an inductance of 4 H. The current through the coil can be calculated using Ohm's Law:
- Current through the coil, IL = V / R = 200 V / 80 Ω = 2.5 A
Behavior Immediately Before Opening the Switch
Before the switch is opened, we have the following values:
- (a) Current through the resistor: 1 A
- (b) Current through the coil: 2.5 A
- (c) E.M.F. induced in the coil: 0 V (since the current is steady and there is no change in current)
- (d) Voltage across the coil: 200 V
Changes After the Switch is Opened
When the switch is opened, the circuit configuration changes. The coil will try to maintain the current flowing through it due to its inductance, which leads to the generation of an induced electromotive force (E.M.F.).
Analyzing the Circuit Immediately After the Switch is Opened
At the moment the switch is opened, the following occurs:
- (a) Current through the resistor: 1 A (remains the same immediately after the switch is opened)
- (b) Current through the coil: 2.5 A (this is the current just before the switch is opened, and it will initially remain the same due to the inductive property)
- (c) E.M.F. induced in the coil: The coil will generate an E.M.F. to oppose the change in current. Using Lenz's Law, the induced E.M.F. can be calculated using the formula: E = -L (di/dt). Since the current is trying to maintain its value, the E.M.F. will be equal to the voltage across the coil, which is 200 V.
- (d) Voltage across the coil: The voltage across the coil will initially be 200 V, as it tries to maintain the current flowing through it.
Summary of Values After the Switch is Opened
To summarize the values immediately after the switch is opened:
- (a) Current through the resistor: 1 A
- (b) Current through the coil: 2.5 A
- (c) E.M.F. induced in the coil: 200 V
- (d) Voltage across the coil: 200 V
This analysis illustrates how inductance plays a crucial role in maintaining current flow immediately after a circuit change, demonstrating the principles of electromagnetic induction and circuit behavior. If you have any further questions or need clarification on any point, feel free to ask!
